Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 829–840

HORIZONTAL CURVATURES AND CLASSIFICATION RESULTS

Chiara Guidi and Vittorio Martino

Università di Bologna, Dipartimento di Matematica
Piazza di Porta S. Donato 5, 40126 Bologna, Italy; chiara.guidi12 'at' unibo.it

Università di Bologna, Dipartimento di Matematica
Piazza di Porta S. Donato 5, 40126 Bologna, Italy; vittorio.martino3 'at' unibo.it

Abstract. In this paper we consider the horizontal high-order curvatures of a real hypersurface in a generic Kähler manifold and we prove a rigidity result under a suitable assumption of parallelism. As an application we get a classification result for hypersurfaces in a complex space form.

2010 Mathematics Subject Classification: Primary 32V40; Secondary 53C55.

Key words: η-umbilical hypersurfaces, complex space forms, H-convexity.

Reference to this article: C. Guidi and V. Martino: Horizontal curvatures and classification results. Ann. Acad. Sci. Fenn. Math. 45 (2020), 829–840.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4541