The Dirac operator on space forms of positive curvature

Shape Operator of Slant Submanifolds in Kenmotsu Space Forms

The First Dirac Eigenvalue on Manifolds with Positive Scalar Curvature

We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich’s eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably.

On the Space of Metrics with Invertible Dirac Operator

On a compact spin manifold we study the space of Riemannian metrics for which the Dirac operator is invertible. The first main result is a surgery theorem stating that such a metric can be extended over the trace of a surgery of codimension at least three. We then prove that if non-empty the space of metrics with invertible Dirac operators is disconnected in dimensions n ≡ 0, 1, 3, 7 mod 8, n ≥...

σk-SCALAR CURVATURE AND EIGENVALUES OF THE DIRAC OPERATOR

On a 4-dimensional closed spin manifold (M, g), the eigenvalues of the Dirac operator can be estimated from below by the total σ2-scalar curvature of M 4 as follows λ 4 ≥ 32 3 R M4 σ2(g)dvol(g) vol(M, g) . Equality implies that (M, g) is a round sphere and the corresponding eigenspinors are Killing spinors. Dedicated to Professor Wang Guangyin on the occasion of his 80th birthday

shape operator of slant submanifolds in kenmotsu space forms