Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

Language: English

You searched for subject:(almost contact geometry). One record found.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


University of South Africa

1. Tshikunguila, Tshikuna-Matamba. The differential geometry of the fibres of an almost contract metric submersion .

Degree: 2013, University of South Africa

Almost contact metric submersions constitute a class of Riemannian submersions whose total space is an almost contact metric manifold. Regarding the base space, two types are studied. Submersions of type I are those whose base space is an almost contact metric manifold while, when the base space is an almost Hermitian manifold, then the submersion is said to be of type II. After recalling the known notions and fundamental properties to be used in the sequel, relationships between the structure of the fibres with that of the total space are established. When the fibres are almost Hermitian manifolds, which occur in the case of a type I submersions, we determine the classes of submersions whose fibres are Kählerian, almost Kählerian, nearly Kählerian, quasi Kählerian, locally conformal (almost) Kählerian, Gi-manifolds and so on. This can be viewed as a classification of submersions of type I based upon the structure of the fibres. Concerning the fibres of a type II submersions, which are almost contact metric manifolds, we discuss how they inherit the structure of the total space. Considering the curvature property on the total space, we determine its corresponding on the fibres in the case of a type I submersions. For instance, the cosymplectic curvature property on the total space corresponds to the Kähler identity on the fibres. Similar results are obtained for Sasakian and Kenmotsu curvature properties. After producing the classes of submersions with minimal, superminimal or umbilical fibres, their impacts on the total or the base space are established. The minimality of the fibres facilitates the transference of the structure from the total to the base space. Similarly, the superminimality of the fibres facilitates the transference of the structure from the base to the total space. Also, it is shown to be a way to study the integrability of the horizontal distribution. Totally contact umbilicity of the fibres leads to the asymptotic directions on the total space. Submersions of contact CR-submanifolds of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are studied. Certain distributions of the under consideration submersions induce the CR-product on the total space. Advisors/Committee Members: Batubenge, T. A (advisor), Massamba, F (advisor).

Subjects/Keywords: Differential Geometry; Riemannian submersions; Almost contact metric submersions; CR-submersions; Contact CR-submanifolds; Almost contact metric manifolds; Almost Hermitian manifolds; Riemannian curvature tensor; Holomorphic sectional curvature; Minimal fibres; Superminimal fibres; Umbilicity

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Tshikunguila, T. (2013). The differential geometry of the fibres of an almost contract metric submersion . (Doctoral Dissertation). University of South Africa. Retrieved from http://hdl.handle.net/10500/18622

Chicago Manual of Style (16th Edition):

Tshikunguila, Tshikuna-Matamba. “The differential geometry of the fibres of an almost contract metric submersion .” 2013. Doctoral Dissertation, University of South Africa. Accessed December 01, 2020. http://hdl.handle.net/10500/18622.

MLA Handbook (7th Edition):

Tshikunguila, Tshikuna-Matamba. “The differential geometry of the fibres of an almost contract metric submersion .” 2013. Web. 01 Dec 2020.

Vancouver:

Tshikunguila T. The differential geometry of the fibres of an almost contract metric submersion . [Internet] [Doctoral dissertation]. University of South Africa; 2013. [cited 2020 Dec 01]. Available from: http://hdl.handle.net/10500/18622.

Council of Science Editors:

Tshikunguila T. The differential geometry of the fibres of an almost contract metric submersion . [Doctoral Dissertation]. University of South Africa; 2013. Available from: http://hdl.handle.net/10500/18622

.