A NEW LICHNEROWICZ-OBATA ESTIMATE IN THE PRESENCE OF A PARALLEL P -FORM Jean-Franc¸ois GROSJEAN To appear in Manuscripta Mathematica, 107, 503-520 (2002) Address: GROSJEAN Jean-Francois, Institut Elie Cartan (Mathematiques), Univer- site Henri Poincare Nancy I, B.P. 239, F-54506 VANDOEUVRE-LES-NANCY CEDEX, FRANCE. E-mail: Abstract Let (Mn, 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 (Mn, 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 (Mn, g) is simply connected. 1
- quaternionic space
- let
- ricm ≥
- trivial parallel
- ricci curvature
- without boundary
- parallel subbun
- quaternionic manifolds
- riemannian connection
- dimensional riemannian