| In this paper, we mainly investigate three questions:the first one is a sufficient and necessary condition for a simply connected Riemannian manifold (Mn,g) to be isometri-cally immersed into Sk×Hn+p-k; the second one is a sufficient and necessary condition for a simply connected Riemannian manifold(Mn,g) to be isometrically immersed into Sk×Sn+p-k; the third one is a sufficient and necessary condition for a simply connected Riemannian manifold (Mn,g) to be isometrically immersed into Hk×Hn+p-k.The dissertation is organized as follows:In the first chapter, above all, we introduce the background of hypersurfaces and submanifolds; then we give some relevant knowledge, such as the formulas of Gauss and Weingarten, the equations of Gauss, Codazzi and Ricci; Finally, we put forward the questions considered in the paper.In the second chapter, we focus on a sufficient and necessary condition for a simply connected Riemannian manifold (Mn, g) to be isometrically immersed into Sk×Hn+p-k.In the third chapter, we focus on a sufficient and necessary condition for a simply connected Riemannian manifold(Mn,g) to be isometrically immersed into Sk×Sn+p-k.In the last chapter, we mainly investigate the third question considered in the pa-per:we focus on a sufficient and necessary condition for a simply connected Riemannian manifold (Mn,g) to be isometrically immersed into Hk×Hn+p-k. |
