The first eigenvalues of finite Riemannian covers

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概要

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• There exists a Riemannian metric on the real projective space such that the first eigenvalue coincides with that of its Riemannian universal cover, if the dimension is bigger than 2. For the proof, we deform the canonical metric on the real projective space. A similar result is obtained for lens spaces, as well as for closed Riemannian manifolds with Riemannian double covers. As a result, on a non-orientable closed manifold other than the real projective plane, there exists a Riemannian metric such that the first eigenvalue coincides with that of its Riemannian double cover.

• 東北大学の論文

著者

• Yoshiji Katsuhiro

  Department Of Mathematics Tokyo Institute Of Technology

関連論文

• The first eigenvalues of finite Riemannian covers
• On the first eigenvalue of non-orientable closed surfaces
• On the Asymptotic Expansion for the Trace of the Heat Kernel on Locally Symmetric Einstein Spaces and its Application

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