p-harmonic 1-forms on totally real submanifolds in complex space forms

Abstract

In this paper, we consider an n-dimensional totally real submanifold M in complex space forms. We establish some vanishing type theorems for $L^Q$ p-harmonic 1-forms on such submanifolds in both cases: either M is minimal; or M is non-minimal.

Keywords:

• Complex space forms
• complex projective spaces
• p-harmonic forms
• totally real submanifolds
• vanishing theorems

AMS Subject Classifications:

• Primary: 53C24
• Secondary: 53C21

Acknowledgments

The authors would like to express their deep thanks to the referee(s) for his/her useful comments that lead to an improvement of the presentation of this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is completed during a stay of the authors at the Vietnam Institute for Advanced Study in Mathematics (VIASM). They would like to thank the staff there for excellent environment and supports. The first author would like to express his gratitude to Prof. Le Minh Ha for constant support. Nguyen Dang Tuyen was funded by Vingroup JSC and supported by the Master, PhD Scholarship Programme of Vingroup Innovation Foundation (VINIF), Institute of Big Data, code VINIF.2021.TS.078.