Geometry of Submanifolds

Prerequisites: Riemannian Geometry (and its prerequisites)

Fundamental equations and the fundamental theorem of isometric immersions. Umbilical and minimal immersions. Convex hypersurfaces. Submanifolds with non-positive sectional curvature. Reduction of codimension. Isometric immersions between spaces of constant sectional curvature. Local isometric rigidity. Global isometric rigidity. Composition of isometric immersions. Conformally flat submanifolds. Conformal immersions. Other topics.

References:
DO CARMO, M. – O Método do Referencial Móvel. Rio de Janeiro, III ELAM, IMPA, 1976.
DAJCZER, M. et al – Submanifolds and Isometric Immersions, Houston, Publish or Perish, 1990.
RODRIGUEZ, L. – Geometria das Subvariedades. Rio de Janeiro, Monografias de Matemática, IMPA, 1976.
SPIVAK, M. – A Comprehensive Introduction to Differential Geometry, Berkeley, Publish or Perish, 1970-75.

* Standard program. The teacher has the autonomy to make any changes