A General Optimal Inequality for Arbitrary Riemannian Submanifolds

نویسندگان

  • BANG-YEN CHEN
  • Bang-Yen Chen
چکیده

One of the most fundamental problems in submanifold theory is to establish simple relationships between intrinsic and extrinsic invariants of the submanifolds (cf. [6]). A general optimal inequality for submanifolds in Riemannian manifolds of constant sectional curvature was obtained in an earlier article [5]. In this article we extend this inequality to a general optimal inequality for arbitrary Riemannian submanifolds in an arbitrary Riemannian manifold. This new inequality involves only the δ-invariants, the squared mean curvature of the submanifolds and the maximum sectional curvature of the ambient manifold. Several applications of this new general inequality are also presented.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Warped Product Semi-Invariant Submanifolds in Almost Paracontact Riemannian Manifolds

We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped product semi-invariant submanifolds in the form N N⊥×fNT by reversing two factor manifolds NT and N⊥. W...

متن کامل

Submanifolds with Parallel Mean Curvature Vector in Pinched Riemannian Manifolds

In this paper, we prove a generalized integral inequality for submanifolds with parallel mean curvature vector in an arbitrary Riemannian manifold, and from which we obtain a pinching theorem for compact oriented submanifolds with parallel mean curvature vector in a complete simply connected pinched Riemannian manifold, which generalizes the results obtained by Alencar-do Carmo and Hong-Wei Xu.

متن کامل

ON THE LIFTS OF SEMI-RIEMANNIAN METRICS

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...

متن کامل

Microsoft Word - art_Andreea_Olteanu_RJM-CS_final

Recently, the author established a general inequality for doubly warped products in arbitrary Riemannian manifolds [14]. In the present paper, we obtain a similar inequality for doubly warped products isometrically immersed in S-space forms. As applications, we derive certain obstructions to the existence of minimal isometric immersions of doubly warped product integral submanifolds in S-space ...

متن کامل

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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005