A Frankel type theorem for CR submanifolds of Sasakian manifolds

Dario Di Pinto and Antonio Lotta

Address:
Dario Di Pinto (corresponding author), Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via E. Orabona 4, 70125 Bari, Italy
Antonio Lotta, Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via E. Orabona 4, 70125 Bari, Italy

E-mail:

Abstract: We prove a Frankel type theorem for $CR$ submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about $CR$ submanifolds of Sasakian space forms.

AMSclassification: primary 53C25; secondary 53C40.

Keywords: intersection of submanifolds, CR submanifold of a Sasakian manifold, scalar Levi form.

DOI: 10.5817/AM2023-5-369