# Makoto KimuraIbaraki University · Department of Mathematics and Informatics

Makoto Kimura

Doctor of Science, 1990, Tokyo Metropolitan Univ.

## About

66

Publications

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Introduction

**Skills and Expertise**

Additional affiliations

April 2012 - present

April 1999 - March 2012

September 1986 - March 1994

Education

April 1984 - August 1986

## Publications

Publications (66)

Let M be a real hypersurface in Pn(C), J be the complex structure and ξ denote a unit normal vector field on M. We show that M is (an open subset of) a homogeneous hypersurface if and only if M has constant principal curvatures and Jξ is principal. We also obtain a characterization of certain complex submanifolds in a complex projective space. Spec...

We prove that a real hypersurface in a non-flat complex space form does not admit
a Ricci soliton whose potential vector field is the Reeb vector field. Moreover,
we classify a real hypersurface admitting so-called “$\eta$-Ricci
soliton” in a non-flat complex space form.

We study Ricci solitons on locally conformally flat hypersurfaces MnMn in space forms M˜n+1(c) of constant sectional curvature cc with potential vector field a principal curvature eigenvector of multiplicity one. We show that in Euclidean space, MnMn is a hypersurface of revolution given in terms of a solution of some non-linear ODE. Hence there ex...

We define Gauss map from a real hypersurface in complex projective space to complex 2-plane Grassmannian. We show that if a real hypersurface is Hopf, then the image of the Gauss map is a half-dimensional totally complex submanifold with respect to quaternionic Kähler structure of complex 2-plane Grassmannian.

We compute sectional curvatures and \(\phi \)-sectional curvatures of homogeneous real hypersurfaces of types (A) and (B) in a complex projective space.

First we introduce the notions of \(\eta \)-parallel and \(\eta \)-commuting shape operator for real hypersurfaces in the complex quadric \(Q^m = SO_{m+2}/SO_mSO_2\). Next we give a complete classification of real hypersurfaces in the complex quadric \(Q^m\) with such kind of shape operators. By virtue of this classification we give a new character...

Along a transversal geodesic γ whose tangent belongs to the contact distribution D, we define the transversal Jacobi operator Rγ=R(·,γ˙)γ˙ on an almost contact Riemannian manifold M. Then, using the transversal Jacobi operator Rγ, we give a new characterization of the Sasakian sphere. In the second part, we characterize the complete ruled real hype...

A ruled real hypersurface in a complex space form is a real hypersurface having a codimension one foliation by totally geodesic complex hyperplanes of the ambient space. Our main purpose of this paper is to introduce a new viewpoint to investigate such hypersurfaces in complex hyperbolic space CHn\documentclass[12pt]{minimal} \usepackage{amsmath} \...

We will give a geometric description of real hypersurfaces with constant ϕ-sectional curvature in complex projective space. Besides geodesic hypersurfaces, such real hypersurfaces are obtained as the image of either a curve or a surface in complex projective space under the polar map. As a consequence, we obtain a classification of real hypersurfac...

We will give a geometric description of real hypersurfaces with constant ϕ-sectional curvature in complex projective space. Besides geodesic hy-persurfaces, such real hypersurfaces are obtained as the image of either a curve or a surface in complex projective space under the polar map. As a consequence, we obtain a classfication of real hypersurfac...

We give a classification of Levi-umbilical real hypersurfaces, whose Levi form is proportional to the induced metric, in the complex two plane Grassmannian G2(Cm+2), the complex quadric Qn, or their noncompact dual spaces.

We wish to attack the problems that H.~Anciaux and K.~Panagiotidou posed in [1], for non-degenerate real hypersurfaces in indefinite complex projective space. We will slightly change these authors' point of view, obtaining cleaner equations for the almost contact metric structure. To make the theory meaningful, we construct new families of non-dege...

In an n-dimensional complex hyperbolic space CHⁿ(c) of constant holomorphic sectional curvature c(< 0), the horosphere HS, which is defined by HS = limr→∞ G(r), is one of nice examples in the class of real hypersurfaces. Here, G(r) is a geodesic sphere of radius r (0 < r < ∞) in CHⁿ(c). The second author ([14]) gave a geometric characterization of...

We construct gradient Ricci solitons as n-dimensional submanifolds in S n × S n by using solutions of some nonlinear ODE.

We characterize the homogeneous ruled real hyperurface of a complex hyperbolic space in the class of ruled real hypersurfaces having constant mean curvature.

We show that Hopf hypersurfaces in complex projective space are constructed from half-dimensional
totally complex submanifolds in complex 2-plane Grssmannian and Legendrian
submanifolds in the twistor space.

We give a classification of Levi-umbilical real hypersurfaces in a complex space form M n (c), n ≥ 3, whose Levi-form is proportional to the induced metric by a non-zero constant. In a complex projective plane CP 2 , we give a local construction of such hypersurfaces and moreover, we give new examples of Levi-flat real hypersurfaces in CP 2 .

We define Gauss map from a real hypersurface in complex hyperbolic space to indefinite complex 2-plane Grassmannian. We show that if a real hypersurface is Hopf, then the image of the Gauss map is a half-dimensional regular submanifold and has a nice behavior under para-quaternionic Kähler structures of the Grassmannian. In particular if absolute v...

In this paper, we study almost contact three-manifolds M whose Ricci operator is invariant along the Reeb flow, that is, M satisfies £ξS=0£ξS=0.

In this paper we study an austere hypersurface M′4 in S5 which is invariant under the action of unit complex numbers S1, i.e., it is the inverse image of a real hypersurface M3 in ℂℙ2. We will give a characterization of a minimal isoparametric hypersurface with 4 distinct principal curvatures in S5. Also we will construct austere hypersurfaces in S...

We classify real hypersurfaces in a
complex space form whose structural reflections are isometries. We also determine real hypersurfaces in a complex
space form whose transversal Jacobi operators have constant eigenvalues and at the same time their eigenspaces
are parallel (along transversal geodesics).

We study curvature of Hopf hypersurfaces in a complex projective space or hyperbolic space. In particular, we prove that there
are no real hypersurfaces in a non-flat complex space form whose Reeb-sectional curvature vanishes.
Mathematics Subject Classification (2000)53B20–53C15–53C25

We study Hopf hypersurfaces in non-flat complex space-forms by using some Gauss maps from a real hypersurface to complex (either positive definite or indefinite) 2-plane Grassmannian and quaternionic (para-)Kähler structures.

If a compact real hypersurface of contact-type in a complex number space admits a Ricci soliton, then it is a sphere. A compact Hopf hypersurface in a non-flat complex space form does not admit a Ricci soliton. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

We show that if ruled Lagrangian submanifold M 3 in 3-dimensional complex Euclidean space is Einstein, then it is flat, provided that the map which gives direction of each ruling has constant rank. Also we give explicit construction of flat ruled Lagrangian submanifolds M 3 in C 3 , from some horizontal curves in S 5 , such that M 3 is neither tota...

We characterize totally η-umbilical hypersurfaces in P 2 ℂ or H 2 ℂ by using the structure Jacobi operator or the Ricci operator.

In this paper we will study compact Lagrangian submanifold M in Kähler manifolds and in particular complex space forms, such that the induced metric on the Lagrangian submanifold is a Ricci soliton with respect to potential vector field given by mean curvature vector field and complex structure.

In this paper we will study compact Lagrangian submanifold M in Kähler manifolds and in particular complex space forms, such that the induced metric on the Lagrangian submanifold is a Ricci soliton with respect to potential vector field given by mean curvature vector field and complex structure.

As a generalization of ruled surfaces, we study Lagrangian submanifolds with 1-parameter family of totally geodesic (n-1)-dimensional totally real, totally geodesic real projective spaces in ℂℙ n .

In this paper, we give a classification of real hypersurfaces in a non-flat complex space form such that the (pseudo-)holomorphic sectional curvatures with respect to the generalized Tanaka-Webster connection are constant.

Existence and $\mathit{SO}(3) \times \mathit{SO}(3)$-congruence
of Lagrangian immersion from oriented 2-dimensional Riemannian
manifold to the Riemannian product of 2-spheres are studied.
In particular, we will show that two minimal Lagrangian immersions
are $\mathit{SO}(3) \times \mathit{SO}(3)$-congruent if and
only if the corresponding angle fun...

. Congruent classes of Frenet curves of order 2 in the complex quadric are studied, obtaining that each congruence class is
a level set of a family of certain smooth functions, that are generalizations of isoparametric functions on the unit sphere
in the tangent space of the complex quadric.

The main purpose of this paper is to survey characterizations of totally umbilic hypersurfaces and isoparametric hypersurfaces related to the results in [T. Adachi and the second author, Czech. Math. J. 55, No. 43, No. 1, 74–78 (2000; Zbl 0964.53044)] and in [the authors, Can. Math. Bull. 43, No. 1, 74–78 (2000; Zbl 0964.53044)].

In this paper we classify real hypersurfaces all of whose geodesics orthogonal to the characteristic vector field are plane curves in complex projective or complex hyperbolic spaces.

In this note we will give a survey of a generalization of Cartan hypersurfaces in sphere.

In this note, we will study about the space of oriented geodesics in hyperbolic spaces Hn. It is well-known that the space of oriented geodesics (i.e., oriented great circles) in spheres Sn is identified with oriented real 2-plane Grassmannian e G2(Rn+1) and complex quadric Qn. We will show that the space of oriented geodesics in Hn is also given s...

We characterize homogeneous real hypersurfaces M's of type (A
1), (A
2) and (B) of a complex projective space in the class of real hypersurfaces by studying the holomorphic distribution T
0
M of M.

We shall provide a characterization of all isoparametric hypersurfacesM's in a real space form ˜ M(c) by observing the extrinsic shape of geodesics of M in the ambient manifold ˜ M(c).

We will give a characterization of all homogeneous real hypersurfaces in a complex projective space by observing the extrinsic shape of geodesics with initial vectors lying in the maximal holomorphic subspace of the tangent space at each point.

Let Pn(C) be an n-dimensional complex projective space with Fubini-Study metric of constant holomorphic sectional curvature 4, and let M be a real hypersurface of Pn(C). M has an almost contact metric structure ... http://www.tulips.tsukuba.ac.jp/mylimedio/dl/page.do?issueid=185629&tocid=100000305&page=547-561

We study real hypersurfaces M of a complex projective space and show that a condition on the derivative of the Ricci Tensor of M implies M is locally homogeneous with two or three principal curvatures.