Isometry actions and geodesics orthogonal to submanifolds

TL;DR

This paper studies special submanifolds in space forms where orthogonal geodesics intersect a fixed submanifold, with applications to horospheres in Hadamard manifolds, revealing geometric intersection properties.

Contribution

It characterizes submanifolds with orthogonal geodesic intersections and applies findings to horospheres in Hadamard manifolds, advancing understanding of geometric structures.

Findings

Characterization of submanifolds with orthogonal geodesic intersection properties

Application to horospheres in Hadamard manifolds

Insights into the geometry of space forms and submanifold interactions

Abstract

We investigate submanifolds in space forms such that every geodesic orthogonal to the submanifold intersects a fixed totally geodesic submanifold. We obtain an application to horospheres in Hadamard manifolds.