Correction to spectral geometry and the Kaehler condition for complex manifolds

Spectral Geometry and the Kaehler Condition for Hermitian Manifolds with Boundary

Let (M, g, J) be a compact Hermitian manifold with a smooth boundary. Let ∆p,B and ⊓ ⊔p,B be the realizations of the real and complex Laplacians on p forms with either Dirichlet or Neumann boundary conditions. We generalize previous results in the closed setting to show that (M, g, J) is Kaehler if and only if Spec(∆p,B) = Spec(2 ⊓ ⊔p,B) for p = 0, 1. We also give a characterization of manifold...

Lecture on Kaehler manifolds

Ricci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds

We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.

Instantons and Kaehler Geometry of Nilpotent Orbits

The first obstacle in building a Geometric Quantization theory for nilpotent orbits of a real semisimple Lie group has been the lack of an invariant polarization. In order to generalize the Fock space construction of the quantum mechanical oscillator, a polarization of the symplectic orbit invariant under the maximal compact subgroup is required. In this paper, we explain how such a polarizatio...

Lectures on complex geometry, Calabi–Yau manifolds and toric geometry

These are introductory lecture notes on complex geometry, Calabi–Yau manifolds and toric geometry. We first define basic concepts of complex and Kähler geometry. We then proceed with an analysis of various definitions of Calabi–Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi–Yau manifolds in two different ways; as hypersurfaces in to...