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Geometry of a weak para-$f$-structure

Authors :
Rovenski, Vladimir
Publication Year :
2023

Abstract

We study geometry of the weak almost para-$f$-structure and its subclasses. This allow us to produce totally geodesic foliations and also to take a fresh look at the para-$f$-structure introduced by A.\,Bucki and A.\,Miernowski. We demonstrate this by generalizing several known results on almost para-$f$-manifolds. First, we express the covariant derivative of $f$ using a new tensor on a metric weak para-$f$-structure, then we prove that on a weak para-${\cal K}$-manifold the characteristic vector fields are Killing and $\ker f$ defines a totally geodesic foliation. Next, we show that a para-${\cal S}$-structure is rigid (i.e., a weak para-${\cal S}$-structure is a para-${\cal S}$-structure), and that a metric weak para-$f$-structure with parallel tensor $f$ reduces to a weak para-${\cal C}$-structure. We obtain corollaries for $p=1$, i.e., for a weak almost paracontact structure.<br />Comment: 13 pages. arXiv admin note: substantial text overlap with arXiv:2205.02158

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2306.03062
Document Type :
Working Paper