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A NEW LICHNEROWICZ OBATA ESTIMATE IN THE PRESENCE OF A PARALLEL P FORM

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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


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A NEW LICHNEROWICZ-OBATA ESTIMATE IN THE PRESENCE OF A PARALLEL P -FORM
Jean-Fran¸coisGROSJEAN To appear in Manuscripta Mathematica, 107, 503-520 (2002)
´ Address:GROSJEANJean-Francois,InstitutElieCartan(Math´ematiques),Univer-sit´eHenriPoincar´eNancyI,B.P.239,F-54506VANDOEUVRE-LES-NANCYCEDEX, FRANCE. E-mail: grosjean@iecn.u-nancy.fr
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.
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