Quite simply, this book offers the most comprehensive survey to date of the theory of semiparallel submanifolds. It begins with the necessary background material, detailing symmetric and semisymmetric Riemannian manifolds, smooth manifolds in space forms, and parallel submanifolds. The book then introduces semiparallel submanifolds and gives some characterizations for their class as well as several subclasses. The coverage moves on to discuss the concept of main symmetric orbit and presents all known results concerning umbilic-like main symmetric orbits. With more than 40 published papers under his belt on the subject, Lumiste provides readers with the most authoritative treatment.[She 2002] Y.-B.Shen, OncompletesubmanifoldswithparallelmeancurvatureinR n +p , in Topology and Geometry: Commemorating SISTAG, Contemporary Mathematics, Vol. ... [Ste 64] S. Sternberg, Lectures on Differential Geometry, PrenticeaHall, Englewood Cliffs, NJ, 1964; 2nd ed., Chelsea, New York, 1983. ... [ Ts 85a] K. Tsukada, Parallel Kaehler submanifolds of Hermitian symmetric spaces, Math.
|Title||:||Semiparallel Submanifolds in Space Forms|
|Publisher||:||Springer Science & Business Media - 2009-03-02|