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 …

" Pseudo-Riemannian geometry is an active research field not only in differential geometry
but also in mathematical physics where the higher signature geometries play a role in brane …

Let M n be a Riemannian manifold and R its curvature tensor. For a point p∈ M n and a unit
vector X∈ T p M n, the Jacobi operator is defined by RX= R (X,·) X. The manifold M n is …

Starting from g g-natural pseudo-Riemannian metrics of suitable signature on the unit
tangent sphere bundle T_1 MT 1 M of a Riemannian manifold (M, ⟨, ⟩)(M,⟨,⟩), we construct …

arXiv:math/0507556v1 [math.DG] 27 Jul 2005 Page 1 arXiv:math/0507556v1 [math.DG] 27 Jul
2005 Four-dimensional Osserman metrics with nondiagonalizable Jacobi operators∗ J. Carlos …

We introduce a new potential characterization of Osserman algebraic curvature tensors. An
algebraic curvature tensor is Jacobi-orthogonal if JXY⊥ JYX holds for all X⊥ Y, where J …

We construct a three-parameter family of contact metric structures on the unit tangent sphere
bundle T 1 M of a Riemannian manifold M and we study some of their special properties …

For a Riemannian manifold $ M^ n $ with the curvature tensor $ R $, the Jacobi operator $
R_X $ is defined by $ R_XY= R (X, Y) X $. The manifold $ M^ n $ is called {\it pointwise …

We give the necessary and sufficient conditions for Jacobi operators that determine an
algebraic curvature tensor. This motivates us to introduce the new concept of Jacobi …

Totally geodesic submanifolds of Damek–Ricci spaces Page 1 Rev. Mat. Iberoam. 37 (2021),
no. 4, 1321–1332 doi 10.4171/rmi/1228 c 2020 Real Sociedad Matemática Espanola Published …