scholarly journals FLATTENED INFINITESIMAL TRANSFORMATIONS OF THE TANGENT BUNDLE WITH HORIZONTAL LIFT CONNECTION, GENERATED BY INFINITESIMAL HOLOMORPHICALLY PROJECTIVE TRANSFORMATIONS

2017 ◽  
Author(s):  
K. M. Zubrilin ◽  
Keyword(s):  
Tangent Bundle ◽  
Horizontal Lift ◽  
Projective Transformations ◽  
Infinitesimal Transformations

Horizontal Lifts of some Geometric Objects to the Bundle of Pairs of Volume Forms

2013 ◽  
Vol 59 (2) ◽  
pp. 357-372
Author(s):  
Anna Gąsior
Keyword(s):  
Vector Fields ◽  
Complex Structure ◽  
Riemannian Metrics ◽  
Almost Complex Structure ◽  
Horizontal Lift ◽  
Almost Complex ◽  
Geometric Objects ◽  
Volume Forms ◽  
Infinitesimal Transformations

Abstract In this paper we present a bundle of pairs of volume forms V2. We describe horizontal lift of a tensor of type (1; 1) and we show that horizontal lift of an almost complex structure on a manifold M is an almost complex structure on the bundle V2. Next we give conditions under which the almost complex structure on V 2 is integrable. In the second part we find horizontal lift of vector fields, tensorfields of type (0; 2) and (2; 0), Riemannian metrics and we determine a family of a t-connections on the bundle of pairs of volume forms. At the end, we consider some properties of the horizontally lifted vector fields and certain infinitesimal transformations.

scholarly journals Infinitesimal Transformations of Locally Conformal Kähler Manifolds

2019 ◽  
Author(s):  
Yevhen Cherevko ◽  
Volodymyr Berezovski ◽  
Irena Hinterleitner ◽  
Dana Smetanová
Keyword(s):  
Partial Differential Equations ◽  
Sufficient Conditions ◽  
Lie Derivative ◽  
Conformal Transformations ◽  
Projective Transformations ◽  
Integrability Conditions ◽  
Necessary And Sufficient ◽  
Locally Conformal ◽  
Lee Form ◽  
Infinitesimal Transformations

The article is devoted to infinitesimal transformations. We have obtained that LCK-manifolds do not admit nontrivial infinitesimal projective transformations. Then we study infinitesimal conformal transformations of LCK-manifolds. We have found the expression for the Lie derivative of a Lee form. Also we have obtained the system of partial differential equations for the transformations, and explored its integrability conditions. Hence we have got the necessary and sufficient conditions in order that the an LCK-manifold admits a group of conformal motions. Also we have calculated the number of parameters which the group depends on. We have proved that a group of conformal motions admitted by an LCK-manifold is isomorphic to a homothetic group admitted by corresponding K\"{a}hlerian metric. We also established that an isometric group of an LCK-manifold is isomorphic to a some subgroup of homothetic group of the coresponding local K\"{a}hlerian metric.

scholarly journals Pseudo-Sasakian manifolds endowed with a contact conformal connection

1986 ◽  
Vol 9 (4) ◽  
pp. 733-747
Author(s):  
Vladislav V. Goldberg ◽  
Radu Rosca
Keyword(s):  
Vector Field ◽  
Lie Algebra ◽  
Tangent Bundle ◽  
Sasakian Manifolds ◽  
Space Forms ◽  
Principal Vector ◽  
Conformal Connection ◽  
Infinitesimal Transformations

Pseudo-Sasakian manifoldsM˜(U,ξ,η˜,g˜)endowed with a contact conformal connection are defined. It is proved that such manifolds are space formsM˜(K),K<0, and some remarkable properties of the Lie algebra of infinitesimal transformations of the principal vector fieldU˜onM˜are discussed. Properties of the leaves of a co-isotropic foliation onM˜and properties of the tangent bundle manifoldTM˜havingM˜as a basis are studied.

scholarly journals Infinitesimal Transformations of Locally Conformal Kähler Manifolds

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 658
Author(s):  
Yevhen Cherevko ◽  
Volodymyr Berezovski ◽  
Irena Hinterleitner ◽  
Dana Smetanová
Keyword(s):  
Sufficient Conditions ◽  
Lie Derivative ◽  
Conformal Transformations ◽  
Projective Transformations ◽  
Integrability Conditions ◽  
Locally Conformal Kähler ◽  
Necessary And Sufficient ◽  
Locally Conformal ◽  
Lee Form ◽  
Infinitesimal Transformations

The article is devoted to infinitesimal transformations. We have obtained that LCK-manifolds do not admit nontrivial infinitesimal projective transformations. Then we study infinitesimal conformal transformations of LCK-manifolds. We have found the expression for the Lie derivative of a Lee form. We have also obtained the system of partial differential equations for the transformations, and explored its integrability conditions. Hence we have got the necessary and sufficient conditions in order that the an LCK-manifold admits a group of conformal motions. We have also calculated the number of parameters which the group depends on. We have proved that a group of conformal motions admitted by an LCK-manifold is isomorphic to a homothetic group admitted by corresponding Kählerian metric. We also established that an isometric group of an LCK-manifold is isomorphic to some subgroup of the homothetic group of the coresponding local Kählerian metric.

Golden Riemannian structures on the tangent bundle with g-natural metrics

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2543-2554
Author(s):  
E. Peyghan ◽  
F. Firuzi ◽  
U.C. De
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Riemannian Metric

Starting from the g-natural Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g), we construct a family of the Golden Riemannian structures ? on the tangent bundle (TM,G). Then we investigate the integrability of such Golden Riemannian structures on the tangent bundle TM and show that there is a direct correlation between the locally decomposable property of (TM,?,G) and the locally flatness of manifold (M,g).

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