J. Korean Math. Soc. 2014; 51(5): 881-895
Printed September 1, 2014
https://doi.org/10.4134/JKMS.2014.51.5.881
Copyright © The Korean Mathematical Society.
Domenico Perrone
Via Provinciale Lecce-Arnesano
In a recent paper \cite{DrPeNew} we introduced the notion of {\em Levi harmonic} map $f$ from an almost contact semi-Riemannian manifold $(M,\varphi,\xi$, $\eta,g)$ into a semi-Riemannian manifold $M^\prime$. In particular, we computed the tension field $\tau_{\mathcal H}(f)$ for a $CR$ map $f$ between two almost contact semi-Riemannian manifolds satisfying the so-called $\varphi$-{\em condition}, where ${\mathcal H} = {\rm Ker}(\eta )$ is the Levi distribution. In the present paper we show that the condition $(A)$ of Rawnsley \cite{Ra} is related to the $\varphi$-condition. Then, we compute the tension field $\tau_{\mathcal H}(f)$ for a $CR$ map between two arbitrary almost contact semi-Riemannian manifolds, and we study the concept of Levi pluriharmonicity. Moreover, we study the harmonicity on quasi-cosymplectic manifolds.
Keywords: almost contact semi-Riemannian manifold, $\varphi$-condition, CR map, invariant submanifold, Levi harmonicity, Levi pluriharmonicity
MSC numbers: 53C43, 53D15, 32V05, 53C25, 53C50, 53C40
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd