Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature [PDF]
Mathematics, 2018 We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold.
Adela Mihai, Ion Mihai
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Some Curvature Characterizations for Hessian Manifolds with Constant Hessian Sectional Curvature [PDF]
Journal of the Institute of Science and Technology, 2017 N , Hessian manifoldunun kompakt bir hiperyuzeyi olsun. Once Hessian manifold konsepti hakkinda bilgi verecegiz sonra ikinci temel tensoru kullanarak sabit Hessian kesit egrilikli Hessian manifoldlari icin bazi egrilik karakterizasyonalari elde ...
Münevver YILDIRIM YILMAZ
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A Note on Pseudo-Umbilical Submanifolds of Hessian Manifolds with Constant Hessian Sectional Curvature [PDF]
ISRN Geometry, 2011 The geometry of Hessian manifold, as a branch of statistics, physics, Kaehlerian, and affine differential geometry, is deeply fruitful and a new field for scientists. However, inspite of its importance submanifolds and curvature conditions of it have not been so well known yet.
Yilmaz, Münevver Yildirim +1 more
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Mathematics, 2022 The geometry of Hessian manifolds is a fruitful branch of physics, statistics, Kaehlerian and affine differential geometry. The study of inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature was truly initiated in ...
Aliya Naaz Siddiqui +2 more
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Hessian manifolds of nonpositive constant Hessian sectional curvature [PDF]
Tohoku Mathematical Journal, 2013 We classify the maximal Hessian manifolds of constant Hessaian sectional curvature nonpositive.
Hitoshi Furuhata, Takashi Kurose
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The δ(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature [PDF]
Entropy, 2020 We establish Chen inequality for the invariant δ ( 2 , 2 ) on statistical submanifolds in Hessian manifolds of constant Hessian curvature. Recently, in co-operation with Chen, we proved a Chen first inequality for such submanifolds.
Adela Mihai, Ion Mihai
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Hessian manifolds of constant Hessian sectional curvature
Journal of the Mathematical Society of Japan, 1995 Let \(M\) be a flat affine manifold with a flat affine connection \(D\). If \(M\) admits a Riemannian metric \(g\) such that \(g\) is locally expressed by \(g= D^2 u\), then \((M, D, g)\) is said to be a Hessian manifold. We define Hessian sectional curvatures (these correspond to holomorphic sectional curvatures for Kählerian manifolds) and construct ...
Hirohiko Shima
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On Hypersurfaces of Hessian Manifolds with Constant Hessian Sectional Curvature [PDF]
Journal of Mathematics and Statistics, 2005 In this study, we give one instrinsic inequality for Riemannian hypersurfaces in Hessian manifolds and sufficient and necessary condition for such hypersurfaces to be totally geodesic.
Mehmet Bektas +2 more
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Shape operator for real space forms in Hessian manifolds of constant Hessian sectional curvature
International Journal of Contemporary Mathematical Sciences, 2007 M. Yildirim Yilmaz, M. Bektas
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Shape-driven confluent rigidity transition in curved biological tissues. [PDF]
Biophys J, 2023 Thomas EC, Hopyan S.
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