关于一类不定复射影空间中全实类空子流形若干问题研究.pdfVIP

On the Study of Totally Real Spacelike Submanifolds of a Class of Indefinite Com plex Projective Space A b s t r a c t Indefinite complex projective space and its to ta lly real spacelike submanifolds are of supreme importance in the study of differentiable geometry. In this thesis, we m ainly study the to ta lly real spacelike submanifolds of a special class of indefinite complex projective space. Under the basic assumption th a t the sectional curvature is constant, we get several conditions for the existence of m axim al immersions from the to ta lly real spacelike submanifolds and the submanifolds’ character by calculating. Besides, we also constitute some Ricci inqualities and Chen inqualities on the to ta lly real spacelike submanifolds. This thesis is made up of 3 chapters: In the 1st chapter, we m ainly introduce the development background and situa­ tion of the differentiable geometry, introduce the provenance and the research signif­ icance of the indefinite complex projective space, provide the main knowledge which we use and the main work of this thesis. In the 2nd chapter, we m ainly use the moving frame method to research the to ta lly real spacelike submanifolds of a class of indefinite complex projective space in detail. Firstly, we get a necessary condition for the existence of m axim al immersions from a to ta lly real spacelike 2-harmonic submanifold having a mean curvature vec­ to r into the indefinite complex projective space by calculating and using the