ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 58 Cristea, Valentin Gabriel, University “ Al. I. Cuza ” of Jassy, Targoviste, Romania Totally umbilical graded submanifolds Totally umbilical graded submanifolds are considered in a superspace of constant supercurvature. A totally umbilical graded submanifold (Y, B) in a superspace ((X, A), G) of constant supercurvature k is also of constant supercurvature. A characterization theorem for a totally umbilical graded submanifold (Y, B) of dimension (s, t) in a superspace form R^{m,n}(k) is given. Reference: 1) B. Kostant, Graded manifolds, graded Lie theory and prequantization, Lect. Notes in Math. no. 570, Springer-Verlag 1977.

2) Bang-Yen Chen, Geometry of submanifolds, Marcel Dekker, Inc. New York 1973.