To find the simple relationship between the extrinsic and intrinsic invariants of submanifold is one of the basic problems in submanifold theory.B.-Y.Chen established inequalities in this respect,called Chen inequalities.The main intrinsic invariants include Chen’s δ-invariant,scalar curvature,Ricci curvature,K-Ricci curvature and so on.The main extrinsic invariants are squared mean curvature and shape operator.Chen inequalities include Chen’s first inequality,Chen’s Ricci inequalities and so on... 

【文章來(lái)源】：南京理工大學(xué)江蘇省 211工程院校

【文章頁(yè)數(shù)】：43 頁(yè)

【學(xué)位級(jí)別】：碩士

【文章目錄】：
Abstract
Chapter 1 Introduction
    1.1 Riemannian Manifolds
    1.2 Symmetric connection
    1.3 Semi-Symmetric connection
    1.4 Semi-Symmetric metric connection
    1.5 Semi-Symmetric non-metric connection
    1.6 Chen's first inequality
Chapter 2 Preliminaries
Chapter 3 Main works
    3.1 Inequalities with respect to Semi-Symmetric metric connection
        3.1.1 Chen first inequality
        3.1.2 Ricci and k-Ricci curvature
    3.2 Inequalities for Semi-Symmetric Non-mctric connection
        3.2.1 Chen's first inequality
        3.2.2 Ricci curvature and k-Ricci Curvatures
Acknowledgements
Bibliography


【參考文獻(xiàn)】：
期刊論文
[1]SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN’S INEQUALITY[J]. 李光漢,吳傳喜.  Acta Mathematica Scientia. 2005(02)



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