Generalized Wintgen Inequality for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature
نویسندگان
چکیده
The geometry of Hessian manifolds is a fruitful branch physics, statistics, Kaehlerian and affine differential geometry. study inequalities for statistical submanifolds in constant curvature was truly initiated 2018 by Mihai, A. I. who dealt with Chen-Ricci Euler inequalities. Later on, Siddiqui, A.N., Ahmad K. Ozel C. came the Casorati inequality same ambient space using algebraic technique. Also, Chen, B.-Y., obtained Chen first such submanifolds. In 2020, studied δ(2,2)-invariant. development this topic, we establish generalized Wintgen curvature. Some examples are also discussed at end.
منابع مشابه
integral inequalities for submanifolds of hessian manifolds with constant hessian sectional curvature
in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.
متن کاملClassification of Totally Umbilical CR-Statistical Submanifolds in Holomorphic Statistical Manifolds with Constant Holomorphic Curvature
In 1985, Amari [1] introduced an interesting manifold, i.e., statistical manifold in the context of information geometry. The geometry of such manifolds includes the notion of dual connections, called conjugate connections in affine geometry, it is closely related to affine geometry. A statistical structure is a generalization of a Hessian one, it connects Hessian geometry. In the present paper...
متن کاملStatistical cosymplectic manifolds and their submanifolds
In this paper, we introduce statistical cosymplectic manifolds and investigate some properties of their tensors. We define invariant and anti-invariant submanifolds and study invariant submanifolds with normal and tangent structure vector fields. We prove that an invariant submanifold of a statistical cosymplectic manifold with tangent structure vector field is a cosymplectic and minimal...
متن کاملThe curvature of a Hessian metric
In this paper, inspired by P.M.H. Wilson’s paper on sectional curvatures of Kähler moduli [31], we concentrate on the case where f is a homogeneous polynomial (also called a “form”) of degree d at least 2. Following Okonek and van de Ven [23], Wilson considers the “index cone,” the open subset where the Hessian matrix of f is Lorentzian (that is, of signature (1, ∗)) and f is positive. He restr...
متن کاملThe Pontryagin Forms of Hessian Manifolds
We show that Hessian manifolds of dimensions 4 and above must have vanishing Pontryagin forms. This gives a topological obstruction to the existence of Hessian metrics. We find an additional explicit curvature identity for Hessian 4-manifolds. By contrast, we show that all analytic Riemannian 2-manifolds are Hessian.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2022
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math10101727