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# How to compute the first eigenvalue of Hyperbolicconeover$${S^n}\left({\frac{1}{2}} \right)$$[M=R\times{}_{\cosht}N\]

$${S^n}\left( M = R \times N$$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?

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# 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 $${S^n}\left( {\frac{1}{2}} \right)$$.