Extension theorems for reductive group actions on compact Kaehler manifolds

Lecture on Kaehler manifolds

Borsuk-ulam Type Theorems for Compact Lie Group Actions

Borsuk-Ulam type theorems for arbitrary compact Lie group actions are proven. The transfer plays a major role in this approach. We present Borsuk-Ulam type theorems for arbitrary compact Lie group actions. The essence of our approach is a generalization of the ideal-valued index of FadellHusseini [FH88] using transfer [Boa66], [BG75], [Dol76], [KP72], [Rou71]. Once an appropriate concept (Defin...

Lie group actions on compact

Let G be a homotopically trivial and effective compact Lie group action on a compact manifold N of nonpositive curvature. Under certain assumptions on N we prove that if G has dimension equal to rank of Center π1(N), then G must be connected. Furthermore, if on N there exists a point having negative definite Ricci tensor, then we show that G is the trivial group.

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.

Linear Models for Reductive Group Actions on Affine Quadrics

RÉSUMÉ. — Nous étudions les actions des groupes réductifs sur les quadriques affines complexes dont le quotient est de dimension 1. Une telle action est dite linéarisable si elle est équivalente à la restriction d’une action linéaire orthogonale dans l’espace affine ambiant de la quadrique. Une action linéaire satisfait à certaines conditions topologiques. Nous recherchons si ces conditions son...