A Frankel type theorem for generic submanifolds of Sasakian manifolds

TL;DR

This paper introduces a new, weaker notion of generic submanifolds in Sasakian manifolds and proves a Frankel type theorem relating to their intersections, providing topological insights into these structures.

Contribution

It defines a weaker genericity condition and establishes a Frankel type theorem for such submanifolds in Sasakian manifolds, extending previous intersection results.

Findings

Proves intersection properties between generic and invariant submanifolds.

Derives topological consequences for generic submanifolds in Sasakian space forms.

Establishes conditions on scalar Levi forms for the theorem.

Abstract

We introduce a weaker notion of generic submanifold of a Sasakian manifold and we prove a Frankel type theorem for this kind of submanifolds under suitable hypotesis on the index of the scalar Levi forms determined by normal directions. It concerns the intersection between a generic and an invariant submanifold and the intersection between two generic submanifolds. From this theorem we derive some topological information about generic submanifolds of Sasakian space forms.