An Optimal Inequality for the Normal Scalar Curvature in Metallic Riemannian Space Forms
نویسندگان
چکیده
In this paper, we prove the DDVV conjecture for a slant submanifold in metallic Riemannian space forms with semi-symmetric metric connection. The equality case of derived inequality is discussed, and some special cases are given.
منابع مشابه
Umbilicity of (Space-Like) Submanifolds of Pseudo-Riemannian Space Forms
We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...
متن کاملRemark about Scalar Curvature and Riemannian Submersions
We consider modified scalar curvature functions for Riemannian manifolds equipped with smooth measures. Given a Riemannian submersion whose fiber transport is measure-preserving up to constants, we show that the modified scalar curvature of the base is bounded below in terms of the scalar curvatures of the total space and fibers. We give an application concerning scalar curvatures of smooth lim...
متن کاملScalar Curvature, Killing Vector Fields and Harmonic One-forms on Compact Riemannian Manifolds
It is well known that no non-trivial Killing vector field exists on a compact Riemannian manifold of negative Ricci curvature; analogously, no non-trivial harmonic one-form exists on a compact manifold of positive Ricci curvature. One can consider the following, more general, problem. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorems canno...
متن کاملumbilicity of (space-like) submanifolds of pseudo-riemannian space forms
we study umbilic (space-like) submanifolds of pseudo-riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo euclidean space and relate this notion to umbilicity. finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.a pseudo-riemannian submanifold m in (a ps...
متن کاملProof of the Normal Scalar Curvature Conjecture
where {e1, · · · , en} (resp. {ξ1, · · · , ξm}) is an orthonormal basis of the tangent (resp. normal) bundle, and R (resp. R) is the curvature tensor for the tangent (resp. normal) bundle. In the study of submanifold theory, De Smet, Dillen, Verstraelen, and Vrancken [5] made the following normal scalar curvature conjecture: Conjecture 1. Let h be the second fundamental form, and let H = 1 n tr...
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: 2023
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math11102252