${\rm SL}(2,\,{\bf C})$ actions on compact Kaehler manifolds

Lecture on Kaehler manifolds

The Fbi Transform on Compact C∞ Manifolds

We present a geometric theory of the Fourier-Bros-Iagolnitzer transform on a compact C∞ manifold M . The FBI transform is a generalization of the classical notion of the wave-packet transform. We discuss the mapping properties of the FBI transform and its relationship to the calculus of pseudodifferential operators on M . We also describe the microlocal properties of its range in terms of the “...

Isometric actions of Heisenberg groups on compact Lorentz manifolds

We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions—those for which the dimension of the Heisenberg group is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the assumption they are real-ana...

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.

Surgery on Compact Manifolds