Invariant submanifolds


Thesis Type: Postgraduate

Institution Of The Thesis: Uludağ Üniversitesi, Turkey

Approval Date: 2005

Thesis Language: Turkish

Student: ÜLKÜ ULUTAŞ

Supervisor: CENGİZHAN MURATHAN

Abstract:

In this thesis we consider Riemannian manifolds, Riemannian product manifolds,on the manifolds so invariant and semi invariant submanifolds and curvatures. This study consists of six chapters. The first chapter is introduction. In the second chapter, some basic definitions and notions which will be used in other chapters are given. In the third chapter, some examples of Riemanniann product manifolds are given. In the fourth chapter, the vertical and horizontal distributions of an invariant submanifold of a Riemannian product manifold and on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form are investigated. In the fifth chapter, necessary and sufficient conditions are given on a semiinvariant submanifold of a Riemann product manifold to be a locally Riemannian manifold.As well fundamental properties of these submanifolds are investigated such as integrability of distributions, totally umbilical semi-invariant submanifold. In the sixth chapter, the Riemannian curvature tensor and the RiemannianChristoffel curvature tensor of a product Riemannian manifold are given.