Gallot-Tanno theorem for pseudo-Riemannian metrics and a proof that decomposable cones over closed complete pseudo-Riemannian manifolds do not exist

Abstract

We generalize for pseudo-Riemannian metrics a classical result of Gallot and Tanno and use it to reprove a recent result of Alekseevsky, Cortes, Galaev and Leistner that decomposable cones over complete closed pseudo-Riemannian manifolds do not exist.

6 pages, no figures

References in corpus (2)

• Complete Einstein metrics are geodesically rigid
• There are no conformal Einstein rescalings of complete pseudo-Riemannian Einstein metrics

Cited by in corpus (8)

• Proof of projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two
• Gallot-Tanno Theorem for closed incomplete pseudo-Riemannian manifolds and applications
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• Conification construction for Kaehler manifolds and its application in c-projective geometry
• Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics
• Rigid supersymmetry, conformal coupling and twistor spinors
• Geometry and holonomy of indecomposable cones
• Semi-Riemannian cones