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AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD

  • S. IVANOV (a1) and D. VASSILEV (a2)

Abstract

We prove the CR version of the Obata's result for the first eigenvalue of the sub-Laplacian in the setting of a compact strictly pseudoconvex pseudohermitian three-dimensional manifold with non-negative CR-Paneitz operator which satisfies a Lichnerowicz-type condition. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value, then, up to a homothety of the pseudohermitian structure, the manifold is the standard Sasakian three-dimensional unit sphere.

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References

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AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD

  • S. IVANOV (a1) and D. VASSILEV (a2)

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