An Intrinsic Approach to Lichnerowicz Conjecture

Proceedings Mathematical Sciences

Akhil Ranjan¹ 

[1] Department of Mathematics, Indian Institute of Technology, Mumbai 00 0, India$$

关键词: Harmonic manifolds;    Blaschke manifold;    mean curvature;    Jacobi differential equation;    Ricci curvature;    compact rank one symmetric spaces;    nice embeddings.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids the nice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial.

【 授权许可】

Unknown