Caner Koca

Vanderbilt University, Nashville, Michigan, United States

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Publications (5)2.13 Total impact

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    Mustafa Kalafat, Caner Koca
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    ABSTRACT: We show that a compact complex surface which admits a conformally K\"ahler metric g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which g becomes a multiple of the Fubini-Study metric.
    Geometriae Dedicata 10/2014; · 0.47 Impact Factor
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    Mustafa Kalafat, Caner Koca
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    ABSTRACT: We show that if a compact complex surface admits a locally conformally flat metric, then it cannot contain a 2-sphere of non-zero self intersection. In particular, the surface has to be minimal. Then we give a list of possibilities.
    05/2013;
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    Mustafa Kalafat, Caner Koca
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    ABSTRACT: We show that a compact complex surface together with an Einstein-Hermitian metric of positive orthogonal bisectional curvature is biholomorphically isometric to the complex projective plane with its Fubini-Study metric up to rescaling. This result relaxes the K\"ahler condition in Berger's theorem, and the positivity condition on sectional curvature in a theorem proved by Koca. The techniques used in the proof are completely different from theirs.
    06/2012;
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    Caner Koca
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    ABSTRACT: In this paper we will prove that the only compact 4-manifold M with an Einstein metric of positive sectional curvature which is also hermitian with respect to some complex structure on M, is the complex projective plane CP^2, with its Fubini-Study metric.
    Proceedings of the American Mathematical Society 12/2011; · 0.61 Impact Factor
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    Caner Koca
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    ABSTRACT: In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach-Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein-Maxwell equations in general relativity. Inspired by the work of C. LeBrun on Einstein-Maxwell equations on compact Kaehler surfaces, we give a variational characterization of solutions to Bach-Merkulov equations as critical points of the Weyl functional. We also show that extremal Kaehler metrics are solutions to these equations, although, contrary to the Einstein-Maxwell analogue, they are not necessarily minimizers of the Weyl functional. We illustrate this phenomenon by studying the Calabi action on Hirzebruch surfaces.
    Journal of Geometry and Physics 12/2011; 70. · 1.06 Impact Factor

Publication Stats

1 Citation
2.13 Total Impact Points

Institutions

  • 2011
    • Vanderbilt University
      • Department of Mathematics
      Nashville, Michigan, United States