Results 211 to 220 of about 112,001 (232)

Hessian Operators on Constraint Manifolds [PDF]

Journal of Nonlinear Science, 2015
On a constraint manifold we give an explicit formula for the Hessian matrix of a cost function that involves the Hessian matrix of a prolonged function and the Hessian matrices of the constraint functions. We give an explicit formula for the case of the orthogonal group ${\bf O}(n)$ by using only Euclidean coordinates on $\mathbb{R}^{n^2}$.
Dan Comanescu, Petre Birtea
exaly   +4 more sources

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 Bektaş
exaly   +2 more sources

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
exaly   +3 more sources

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A Chen First Inequality for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Results in Mathematics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen Bang-yen, Adela Mihai, Ion Mihai
exaly   +3 more sources

Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

2019
In the present paper, we study Hessian and Einstein-Hessian manifolds with some examples. We establish optimizations of the intrinsic invariant (normalized scalar curvature) for a new extrinsic invariant (generalized normalized Casorati curvatures) on statistical submanifolds in a Hessian manifold of constant Hessian curvature by using algebraic ...
Aliya Naaz Siddiqui, Kamran Ahmad, Cenap Özel   +2 more
openaire   +1 more source

A survey on curvatures of Hessian manifolds

Chaos, Solitons & Fractals, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yilmaz, Münevver Yildirim, Bektaş, Mehmet   +1 more
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Hessian Manifolds and Convexity

1981
Let M be a flat affine manifold, that is, M admits open charts (Ui, x i 1 ,..., x i n such that M =U Ui and whose coordinate changes are all affine functions. Such local coordinate systems { i n ,...,x i n } will be called affine local coordinate systems.
openaire   +1 more source

On Hessian Structures on an Affine Manifold

1981
On a smooth manifold, an affine connection whose torsion and curvature vanish identically is called an affine structure. A smooth manifold provided with an affine structure is called an affine manifold. Let M be an affine manifold with an affine structure D. The co-variant differentiation by D will be also denoted by D.
openaire   +1 more source

The δ(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Entropy, 2020
Adela Mihai, Ion Mihai
exaly  

Second Order Estimates for Complex Hessian Equations on Hermitian Manifolds

Discrete and Continuous Dynamical Systems, 2021
Weisong Dong
exaly