scholarly journals New types of almost contact metric submersions

2021 ◽  
Vol 20 ◽  
pp. 345-355
Author(s):  
T.Tshikuna Matamba
Keyword(s):  
Riemannian Submersion ◽  
Contact Geometry ◽  
Base Space ◽  
Almost Contact Metric

We introduce the concept of conjugaison in contact geometry. This concept allows to define new structures which are used as base space of a Riemannian submersion. With these new structures, we study new three types of almost contact metric submersions.

scholarly journals Almost contact metric3-submersions

1984 ◽  
Vol 7 (4) ◽  
pp. 667-688 ◽  
Author(s):  
Bill Watson
Keyword(s):  
Vector Fields ◽  
Betti Numbers ◽  
Riemannian Submersion ◽  
Second Fundamental Form ◽  
Horizontal Distribution ◽  
Total Space ◽  
Field Equations ◽  
Contact Metric Manifold ◽  
Almost Contact Metric ◽  
Weak Structure

An almost contact metric3-submersion is a Riemannian submersion,πfrom an almost contact metric manifold(M4m+3,(φi,ξi,ηi)i=13,g)onto an almost quaternionic manifold(N4n,(Ji)i=13,h)which commutes with the structure tensors of type(1,1);i.e.,π*φi=Jiπ*, fori=1,2,3. For various restrictions on∇φi, (e.g.,Mis3-Sasakian), we show corresponding limitations on the second fundamental form of the fibres and on the complete integrability of the horizontal distribution. Concommitantly, relations are derived between the Betti numbers of a compact total space and the base space. For instance, ifMis3-quasi-Saskian(dΦ=0), thenb1(N)≤b1(M). The respectiveφi-holomorphic sectional and bisectional curvature tensors are studied and several unexpected results are obtained. As an example, ifXandYare orthogonal horizontal vector fields on the3-contact (a relatively weak structure) total space of such a submersion, then the respective holomorphic bisectional curvatures satisfy:Bφi(X,Y)=B′J′i(X*,Y*)−2. Applications to the real differential geometry of Yarg-Milis field equations are indicated based on the fact that a principalSU(2)-bundle over a compactified realized space-time can be given the structure of an almost contact metric3-submersion.

Semi-invariant ξ⊥-Riemannian submersions from almost contact metric manifolds

2017 ◽  
Vol 14 (05) ◽  
pp. 1750074 ◽  
Author(s):  
Mehmet Akif Akyol ◽  
Ramazan Sarı ◽  
Elif Aksoy
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Riemannian Submersions ◽  
Contact Metric Manifolds ◽  
Almost Contact Metric ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Almost Contact Metric Manifolds

As a generalization of anti-invariant [Formula: see text]-Riemannian submersions, we introduce semi-invariant [Formula: see text]-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We give examples, investigating the geometry of foliations which arise from the definition of a Riemannian submersion and proving a necessary and sufficient condition for a semi-invariant [Formula: see text]-Riemannian submersion to be totally geodesic. Moreover, we study semi-invariant [Formula: see text]-Riemannian submersions with totally umbilical fibers.

scholarly journals Neutral signature gauged supergravity solutions

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
J. Gutowski ◽  
W. A. Sabra
Keyword(s):  
Cosmological Constant ◽  
Geometric Structure ◽  
Base Space ◽  
Killing Spinor ◽  
Positive Cosmological Constant ◽  
3 Dimensional

Abstract We classify all supersymmetric solutions of minimal D = 4 gauged supergravity with (2) signature and a positive cosmological constant which admit exactly one Killing spinor. This classification produces a geometric structure which is more general than that found for previous classifications of N = 2 supersymmetric solutions of this theory. We illustrate how the N = 2 solutions which consist of a fibration over a 3-dimensional Lorentzian Gauduchon-Tod base space can be written in terms of this more generic geometric structure.

Triharmonic Riemannian submersions from 3-dimensional space forms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomoya Miura ◽  
Shun Maeta
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Dimensional Space ◽  
Riemannian Submersion ◽  
Partial Answer ◽  
Riemannian Submersions ◽  
Space Forms ◽  
3 Dimensional

Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.

scholarly journals Semi-invariant Riemannian submersions from nearly Kaehler manifolds

2020 ◽  
Vol 17 (07) ◽  
pp. 2050100
Author(s):  
Rupali Kaushal ◽  
Rashmi Sachdeva ◽  
Rakesh Kumar ◽  
Rakesh Kumar Nagaich
Keyword(s):  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Horizontal Distribution ◽  
Product Manifold ◽  
Riemannian Submersions ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Nearly Kaehler Manifold ◽  
The Vertical Distribution ◽  
Usual Product

We study semi-invariant Riemannian submersions from a nearly Kaehler manifold to a Riemannian manifold. It is well known that the vertical distribution of a Riemannian submersion is always integrable therefore, we derive condition for the integrability of horizontal distribution of a semi-invariant Riemannian submersion and also investigate the geometry of the foliations. We discuss the existence and nonexistence of semi-invariant submersions such that the total manifold is a usual product manifold or a twisted product manifold. We establish necessary and sufficient conditions for a semi-invariant submersion to be a totally geodesic map. Finally, we study semi-invariant submersions with totally umbilical fibers.

Contact-geometry engineering in a circular light-emitting diode (LED) for improved electrical and optical performances

2012 ◽  
Vol 28 (1) ◽  
pp. 015006 ◽  
Author(s):  
Yun Soo Park ◽  
Hwan Gi Lee ◽  
Chung-Mo Yang ◽  
Dong-Seok Kim ◽  
Jin-Hyuk Bae ◽  
...  
Keyword(s):  
Light Emitting Diode ◽  
Contact Geometry ◽  
Light Emitting

Quasi-standard C*-algebras

1990 ◽  
Vol 107 (2) ◽  
pp. 349-360 ◽  
Author(s):  
R. J. Archbold ◽  
D. W. B. Somerset
Keyword(s):  
Cross Sections ◽  
Equivalence Relation ◽  
Dense Subset ◽  
Base Space ◽  
Ideal Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
C Algebras ◽  
Necessary And Sufficient ◽  
Full Algebra

AbstactA necessary and sufficient condition is given for a separable C*-algebra to be *-isomorphic to a maximal full algebra of cross-sections over a base space such that the fibre algebras are primitive throughout a dense subset. The condition is that the relation of inseparability for pairs of points in the primitive ideal space should be an open equivalence relation.

Sign in / Sign up

Export Citation Format

Share Document