Sabit Hessian Kesit Eğrilikli Hessian Manifoldları için Bazı Eğrilik Karakterizasyonları

N , Hessian manifoldunun kompakt bir hiperyüzeyi olsun. Önce Hessian manifold konseptihakkında bilgi vereceğiz sonra ikinci temel tensörü kullanarak sabit Hessian kesit eğrilikli Hessian manifoldlarıiçin bazı eğrilik karakterizasyonaları elde edeceğiz

Anahtar Kelimeler:

Hessian manifoldu, kesit eğriliği, ikinci temel form.

Some Curvature Characterizations for Hessian Manifolds with Constant Hessian Sectional Curvature

Let N be a compact hypersurface in the Hessian manifold . We frstly introduceHessian manifold concept then using second fundamental tensor, we obtain some curvature characterizations whichare new for Hessian manifolds with constant Hessian sectional curvature

Keywords:

Hessian manifold, sectional curvature, second fundamental form,

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Bektas M¸ Yıldırım M, 2006. Integral inequalities for submanifolds of Hessian manifolds with constant Hessian sectional curvature. Irania. Jour. of Scien. and Techno. Transact. A, 30(2):235-239.
Camargoa FEC, Chavesa RVB, Sousa Jr LAM, 2008. Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space. Differential Geometry and its Applications. 26(6): 592-599. Caminha A, 2006. A rigidity theorem for complete CMC hypersurfaces in Lorentz manifolds. Diff. Geom. and its Applic.. 24(6):652—659.
Colares AG, De Lima HF, 2002. Some rigidity theorems in semi-Riemannian warped products, Kodai Mathemat. J. 35(2): 268-282.
Ho PT, 2015. Differentiable rigidity of hypersurface in space forms. Manuscripta mathem. 146: 463-472.
Kobayashi, S, Nomizu K, 1969. Foundations of differential geometry, Vols. I, II, Inter science, N. York.
Li, H, 1997. Global rigidity theorems for hypersurfaces. Arkiv Math. 35: 327-351.
Shima H, 1986. Vanishing theorems for compact Hessian manifolds. Annals Institute. Fourier Grenob.. 36(3):183-205.
Shima H, 1995. Hessian manifolds of constant Hessian sectional curvature. Journal of Mathematical Society of Japan. 47(4): 735-753.
Shima H, 2007. The Geometry of Hessian structures. World Scien. Publ., First edition Singapore, Japan. 246p.
Shima H, Yagi, K,. 1997. Geometry of Hessian manifolds, Diﬀerential Geometry and its Applications. 7(3): 277–290.
Yilmaz MY, Bektas¸M, 2008. A survey on curvatures of Hessian manifolds. Chaos, Solit.& Fract. 38(3): 620-630.