Page 362 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 362
GEOMETRIES DEFINED BY DIFFERENTIAL FORMS (MS-44)
The Obata first eigenvalue theorem on a seven dimensional quaternionic
contact manifold
Dimiter Vassilev, vassilev@unm.edu
University of New Mexico, United States
Coauthor: Abdelrahman Mohamed
We give an Obata type rigidity result for the first eigenvalue of the sub-Laplacian. on a compact
seven dimensional quaternionic contact manifold which satisfies a Lichnerowicz-type bound on
its quaternionic contact Ricci curvature and has a non-negative Paneitz P-function. In particular,
under the stated conditions, the lowest possible eigenvalue of the sub-Laplacian is achieved if
and only if the manifold is qc-equivalent to the standard 3-Sasakian sphere.
360
The Obata first eigenvalue theorem on a seven dimensional quaternionic
contact manifold
Dimiter Vassilev, vassilev@unm.edu
University of New Mexico, United States
Coauthor: Abdelrahman Mohamed
We give an Obata type rigidity result for the first eigenvalue of the sub-Laplacian. on a compact
seven dimensional quaternionic contact manifold which satisfies a Lichnerowicz-type bound on
its quaternionic contact Ricci curvature and has a non-negative Paneitz P-function. In particular,
under the stated conditions, the lowest possible eigenvalue of the sub-Laplacian is achieved if
and only if the manifold is qc-equivalent to the standard 3-Sasakian sphere.
360
