JournalsjstVol. 7, No. 4pp. 1119–1170

The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven

  • Stefan Ivanov

    University of Sofia, Bulgaria
  • Alexander Petkov

    University of Sofia, Bulgaria
  • Dimiter Vassilev

    University of New Mexico, Albuquerque, USA
The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven cover
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Abstract

On a compact quaternionic contact (qc) manifold of dimension bigger than seven and satisfying a Lichnerowicz type lower bound estimate we show that if the rst positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of the qc structure, the manifold is qc equivalent to the standard 3-Sasakian sphere. The same conclusion is shown to hold on a non-compact qc manifold which is complete with respect to the associated Riemannian metric assuming the existence of a function with traceless horizontal Hessian.

Cite this article

Stefan Ivanov, Alexander Petkov, Dimiter Vassilev, The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven. J. Spectr. Theory 7 (2017), no. 4, pp. 1119–1170

DOI 10.4171/JST/187