integral inequalities for submanifolds of hessian manifolds with constant hessian sectional curvature
نویسندگان
چکیده
in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.
منابع مشابه
Isoperimetric-type inequalities on constant curvature manifolds
By exploiting optimal transport theory on Riemannian manifolds and adapting Gromov’s proof of the isoperimetric inequality in the Euclidean space, we prove an isoperimetric-type inequality on simply connected constant curvature manifolds.
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 کاملEstimating the Hessian by Back-propagating Curvature
In this work we develop Curvature Propagation (CP), a general technique for efficiently computing unbiased approximations of the Hessian of any function that is computed using a computational graph. At the cost of roughly two gradient evaluations, CP can give a rank-1 approximation of the whole Hessian, and can be repeatedly applied to give increasingly precise unbiased estimates of any or all ...
متن کاملStrictly Kähler-Berwald manifolds with constant holomorphic sectional curvature
In this paper, the authors prove that a strictly Kähler-Berwald manifold with nonzero constant holomorphic sectional curvature must be a Kähler manifold.
متن کاملHigher order Hessian structures on manifolds
In this paper we define nth order Hessian structures on manifolds and study them. In particular, when n = 3, we make a detailed study and establish a one-to-one correspondence between third-order Hessian structures and a certain class of connections on the second-order tangent bundle of a manifold. Further, we show that a connection on the tangent bundle of a manifold induces a connection on th...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
iranian journal of science and technology (sciences)ISSN 1028-6276
دوره 30
شماره 2 2006
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023