HESSIAN GEOMETRY OF THE HOMOGENEOUS GRAPH DOMAIN

Title & Authors
HESSIAN GEOMETRY OF THE HOMOGENEOUS GRAPH DOMAIN
Choi, Yun-Cherl; Chang, Kyeong-Soo;

Abstract
In this paper, we will investigate the Hessian geometry of the homogeneous domain over the hypersurface given by a function F : $\small{\mathbb{R}^n{\rightarrow}\mathbb{R}}$ with ${\mid}{\det}\;DdF\mid Keywords Hessian algebra;Hessian domain;homomgeneous graph domain;Hessian geometry;sectional curvature; Language English Cited by 1. Abelian Hessian algebra and commutative Frobenius algebra, Linear Algebra and its Applications, 2008, 428, 8-9, 2236 2. Affine hypersurfaces with parallel difference tensor relative to affine α-connection, Journal of Geometry and Physics, 2014, 86, 81 References 1. N. Bokan, K. Nomizu, and U. Simon, Affine hypersurfaces with parallel cubic forms, Tohoku Math. J. 42 (1990), no. 2, 101-108 2. Y. Choi and H. Kim, A characterization of Cayley Hypersurface and Eastwood and Ezhov conjecture, Internat. J. Math. 16 (2005), no. 8, 841-861 3. Y. Choi, Nondegenerate affine homogeneous domain over a graph, J. Korean Math. Soc. 43 (2006), no. 6, 1301-1324 4. F. Dillen and L. Vrancken, Hypersurfaces with parallel difference tensor, Japan. J. Math. (N.S.) 24 (1998), no. 1, 43-60 5. F. Dillen, L. Vrancken, and S. Yaprak, Affine hypersurfaces with parallel cubic form, Nagoya Math. J. 135 (1994), 153-164 6. J. Hua Hao and H. Shima, Level surfaces of nondegenerate functions in$R^{n+1}\$, Geom. Dedicata 50 (1994), 193-204

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