Geodesicity and isoclinity properties for the tangent bundle of the Heisenberg manifold with Sasaki metric

Simona-luiza DRUTA; Paola Piu

Article Details

Geodesicity and isoclinity properties for the tangent bundle of the Heisenberg manifold with Sasaki metric

Authors:

Simona-luiza DRUTA | Paola Piu

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2012 Vol.36 Issue 2, pp.331-343

Document Type:

Article

Publication Date:

1/2012

Document Language:

Turkish

Document ID (Org No.):

2000747842

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Keywords:

Abstract:

 

We prove that the horizontal and vertical distributions of  the tangent bundle with the Sasaki metric are isocline, the  distributions given by the kernels of the horizontal and vertical  lifts of the contact form w on the Heisenberg manifold (H3,g) to  (TH3,gS) are not totally geodesic, and the distributions  FH=L(E1H,E2H) and FV=L(E1V,E2V) are totally geodesic, but  they are not isocline.  We obtain that the horizontal and natural  lifts of the curves from the Heisenberg manifold (H3,g), are  geodesics on the tangent bundle endowed with the Sasaki metric  (TH3,gs), if and only if the curves considered on the base manifold  are geodesics.  Then, we get two particular examples of geodesics on  (TH3,gs), which are not horizontal or natural lifts of geodesics  from the base manifold (H3,g).

 

We prove that the horizontal and vertical distributions of  the tangent bundle with the Sasaki metric are isocline, the  distributions given by the kernels of the horizontal and vertical  lifts of the contact form w on the Heisenberg manifold (H3,g) to  (TH3,gS) are not totally geodesic, and the distributions  FH=L(E1H,E2H) and FV=L(E1V,E2V) are totally geodesic, but  they are not isocline.  We obtain that the horizontal and natural  lifts of the curves from the Heisenberg manifold (H3,g), are  geodesics on the tangent bundle endowed with the Sasaki metric  (TH3,gs), if and only if the curves considered on the base manifold  are geodesics.  Then, we get two particular examples of geodesics on  (TH3,gs), which are not horizontal or natural lifts of geodesics  from the base manifold (H3,g).

Article Details

Geodesicity and isoclinity properties for the tangent bundle of the Heisenberg manifold with Sasaki metric

Authors:

Simona-luiza DRUTA | Paola Piu

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2012 Vol.36 Issue 2, pp.331-343

Document Type:

Article

Publication Date:

1/2012

Document Language:

Turkish

Document ID (Org No.):

2000747842

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Tangent bundle

Sasaki metric

Heisenberg metric

geodesics

Issues

Article Details

Geodesicity and isoclinity properties for the tangent bundle of the Heisenberg manifold with Sasaki metric

Authors: Simona-luiza DRUTA | Paola Piu

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2012 Vol.36 Issue 2, pp.331-343

Document Type: Article

Publication Date: 1/2012

Document Language: Turkish

Document ID (Org No.): 2000747842

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Tangent bundle

Sasaki metric

Heisenberg metric

geodesics

Issues

Authors:

Simona-luiza DRUTA | Paola Piu

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2012 Vol.36 Issue 2, pp.331-343

Document Type:

Article

Publication Date:

1/2012

Document Language:

Turkish

Document ID (Org No.):

2000747842

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098