On minimal submanifolds in product manifolds with a certain Riemannian metric
نویسندگان
چکیده
منابع مشابه
Warped Product Submanifolds of Riemannian Product Manifolds
and Applied Analysis 3 where TX and NX are the tangential and normal components of FX, respectively, and for V ∈ T⊥M,
متن کاملWarped 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 کاملInterface Foliation near Minimal Submanifolds in Riemannian Manifolds with Positive Ricci Curvature
Let (M, g̃) be an N -dimensional smooth compact Riemannian manifold. We consider the singularly perturbed Allen-Cahn equation ε∆g̃u + (1− u)u = 0 in M, where ε is a small parameter. Let K ⊂M be an (N − 1)-dimensional smooth minimal submanifold that separatesM into two disjoint components. Assume that K is non-degenerate in the sense that it does not support non-trivial Jacobi fields, and that |AK...
متن کاملSubmanifolds 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 کاملOn totally umbilic submanifolds of semi-Riemannian manifolds
The notion of being totally umbilic is considered for non-degenerate and degenerate submanifolds of semi-Riemanian manifolds. After some remarks on the general case, timelike and lightlike totally umbilic submanifolds of Lorentzian manifolds are discussed, along with their physical interpretation in view of general relativity. In particular, the mathematical notion of totally umbilic submanifol...
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: Tsukuba Journal of Mathematics
سال: 1996
ISSN: 0387-4982
DOI: 10.21099/tkbjm/1496162989