A new Lichnerowicz–Obata estimate in the presence of a parallel p-form |
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Authors: | Grosjean Jean-François |
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Institution: | (1) Institut élie Cartan (Mathématiques), Université Henri Poincaré Nancy I, B.P. 239, F-54506 Vandoeuvre-les-Nancy Cedex, France. e-mail: grosjean@iecn.u-nancy.fr, FR |
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Abstract: | Let (M
n
,g) be a compact Riemannian manifold with a smooth boundary. In this paper, we give a Lichnerowicz-Obata type lower bound for
the first eigenvalue of the Laplacian of (M
n
,g) when M has a parallel p-form (2 ≤p≤n/2). This result follows from a new Bochner-Reilly's formula. Moreover, we give a characterization of the equality case when
(M
n
,g) is simply connected.
Received: 1 June 2001 |
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Keywords: | |
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