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A note on generalized Dirac eigenvalues for split holonomy and torsion

김화정|Ilka Agricola
대한수학회 (The Korean Mathematical Society)|2014.11|대한수학회보 (Bulletin of the KMS)|제51권 제6호|pp. 1579-1589

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참고문헌

키워드

Dirac operatoreigenvalue estimatemetric connection with torsion
주제분류수학

초록

We study the Dirac spectrum on compact Riemannian spin manifolds M equipped with a metric connection ∇ with skew torsion T ∈ 3M in the situation where the tangent bundle splits under the holonomy of ∇ and the torsion of ∇ is of ‘split’ type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich’s classical Riemannian estimate.

Abstract

We study the Dirac spectrum on compact Riemannian spin manifolds M equipped with a metric connection ∇ with skew torsion T ∈ 3M in the situation where the tangent bundle splits under the holonomy of ∇ and the torsion of ∇ is of ‘split’ type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich’s classical Riemannian estimate.

참고문헌 (27)

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