This second edition explores recent progress in the submanifold geometry of space forms,
including new methods based on the holonomy of the normal connection. It contains five …

Problems in submanifold theory have been studied since the invention of calculus and it was
started with differential geometry of plane curves. Owing to his studies of how to draw …

We prove, in a purely geometric way, that there are no connected irreducible proper
subgroups of SO (N, 1). Moreover, a weakly irreducible subgroup of SO (N, 1) must either act …

In [4] it was proved that given a submanifold of Euclidean space the representation on the
normal space of the holonomy group of the normal connection is an^-representation (ie …

arXiv:2408.01645v1 [math.DG] 3 Aug 2024 Page 1 arXiv:2408.01645v1 [math.DG] 3 Aug 2024
HOMOGENEOUS STRUCTURES OF 3-DIMENSIONAL SASAKIAN SPACE FORMS JUN-ICHI …

In this paper we study cohomogeneity one Minkowski space Rn 1. Among other results, we
prove that the orbit space is homeomorphic to R or [0,∞). We show that if there is a …

Abstract Let Mn, n> 2, be an orbit of a representation of a compact Lie group which is
irreducible and full as a submanifold of the ambient space. We prove that if M admits a …

Let G/K be an irreducible Riemannian symmetric space, where G is a connected compact
semisimple Lie group and K its closed subgroup. The adjoint representation group Ad (A^) …

We study the set X [M] of planar normal sections on the natural imbedding of a flag manifold
M. We characterize X [M] and show that it is a real algebraic submanifold of ℝ P n (n= dim …

We survey applications of holonomic methods to the study of submanifold geometry,
showing the consequences of some sort of extrinsic version of de Rham decomposition and …