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April 1984
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251 Reads
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113 Citations
Journal of the Mathematical Society of Japan
We introduced and studied the notions of harmonic metrics and harmonic tensors as well as finding some relationships between harmonic metrics, harmonic tensors, geodesic vector fields, and Gauss map of Euclidean submanifolds.
March 1982
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177 Reads
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38 Citations
Comptes Rendus Mathematique
July 1980
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185 Reads
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114 Citations
Duke Mathematical Journal
One purpose of this article is to establish a general method to determine stability of totally geodesic submanifolds of symmetric spaces. The method is used to determine the stability of the basic totally geodesic submanifolds (M_+,M_)--introduced and studied by B.-Y. Chen and T. Nagano in [Totally geodesic submanifolds of symmetric spaces, II, Duke Math. J. 45 (1978), 405-425] as minimal submanifolds. The other purpose is to establish a stability theorem for minimal totally real submanifolds of Kaehlerian manifolds.
January 1978
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770 Reads
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209 Citations
Duke Mathematical Journal
By using antipodal sets and fixed point sets, we introduce a new method to study compact symmetry spaces. In this paper, we also provide several applications of our method.
December 1977
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1,178 Reads
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331 Citations
Duke Mathematical Journal
By applying Lie triple system we classify totally geodesic submanifolds of complex quadrics Q^n=SO(n+2)/SO(2) x SO(n) for n ≥ 2.
... It is well-known in the theory of designs that a finite subset of a sphere is a tight spherical 1-design if and only if it is a pair of antipodal points. On the other hand, antipodal sets and 2-number for a Riemannian manifold are introduced by B.-Y. Chen and T. Nagano [21] in 1982. An antipodal set is called a great antipodal set if its cardinality is equal to the 2-number. ...
March 1982
Comptes Rendus Mathematique
... Chen and Nagano [8] proved that a simply connected, irreducible symmetric space admits a totally geodesic hypersurface if and only if it is of constant curvature. Tsukada [27] extended this result to the class of simply connected irreducible naturally reductive homogeneous spaces. ...
January 1978
Duke Mathematical Journal
... The problem has been completely solved in the case of the symmetric space G 2 / SO (4). Although some of these submanifolds are missing in the classification by Chen and Nagano in [9], the classification obtained by Sebastian Klein in [18] is complete, based on the reconstruction of the curvature tensor from the Satake diagram previously considered in [16]. Both [9] and [18] are devoted to symmetric spaces of rank 2. We are interested in exceptional symmetric spaces, and, in this topic, the recent reference [20] is relevant and of course it encloses G 2 / SO(4) as a particular case. ...
December 1977
Duke Mathematical Journal
... Since the discovery byÉ Cartan, symmetric spaces, a distinguished class of Riemannian manifolds, attracted the attention of numerous mathematicians from various fields such as differential geometry, algebraic topology, representation theory and harmonic analysis. [19,24,25,26,27,28]). This theory was also known today as the Chen-Nagano theory in some literatures (see, e.g., [90,91]). ...
July 1980
Duke Mathematical Journal
... Univ. Hamburg, 5 (1927), [24][25][26][27][28][29][30][31][32] proved that Any two-knot diagrams belonging to the same knot are related by a sequence of these three moves. ...
April 1984
Journal of the Mathematical Society of Japan
