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Golden-Hessian Structures

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Abstract

Let (M, g) be an \(n-\)dimensional (pseudo)-Riemannian manifold and \( f:M\rightarrow {\mathbb {R}}\) be a smooth function whose Hessian with respect to g is non-degenerate. One can define the associated (pseudo)-Riemannian Hessian metric \(h=\nabla ^{2}f\) on M, where \(\nabla \) is the Levi-Civita connection of g. In the present paper we investigate conditions under which the manifold M equipped with a (complex) golden structure and with the Hessian metric h is a (holomorphic) locally decomposable golden (Norden) Hessian manifold. Furthermore some examples are presented.

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Acknowledgments

Authors would like to thank Professor Mircea Crasmareanu for valuable comments and useful discussions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ataturk University, 25240, Erzurum, Turkey

    Aydin Gezer & Cagri Karaman

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  1. Aydin Gezer
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  2. Cagri Karaman
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Correspondence to Aydin Gezer.

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Gezer, A., Karaman, C. Golden-Hessian Structures. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 86, 41–46 (2016). https://doi.org/10.1007/s40010-015-0226-0

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  • DOI: https://doi.org/10.1007/s40010-015-0226-0

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