$${S^n}\left( $M = R \times N$$with the warped product metric$$d{s^2} = d{t^2} + {\frac{1}{2}} \cosh ^2}\left( t \right)$$denotes an n-dim sphere right)ds_N^2$$where N(dimN=n-1) is a compact manifold with radius 1/2,How $$Ric \ge - \left( {n - 2} \right)$$It should be mentioned that M may not be a Riemannian manifold but an Alexandrov space.So how to compute the first eigenvalue of Hyperbolic cone over M?If we restrict to the case $${S^n}\left( $N = {S^{n - 1}}\left( {\frac{1}{2}} \right)$$.right)$$an n-1 dim sphere with radius 1/2,then the result?
|
2 | added 266 characters in body; edited title; edited body; deleted 1 characters in body | ||
How to compute the first eigenvalue of Hyperbolic cone over $${S^n}\left( {\frac{1}{2}} \right)$$[M = R \times {}_{\cosh t}N\] |
||||
|
|
1 |
|
||
How to compute the first eigenvalue of Hyperbolic cone over $${S^n}\left( {\frac{1}{2}} \right)$$$${S^n}\left( {\frac{1}{2}} \right)$$denotes an n-dim sphere with radius 1/2,How to compute the first eigenvalue of Hyperbolic cone over $${S^n}\left( {\frac{1}{2}} \right)$$.
|
||||
