Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection
We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an η-Einstein manifold. We also investigate some properties of curvature tensor, conformal curvature tensor, W2-curvature tenso...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/395462 |
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| author | Bilal Eftal Acet Erol Kılıç Selcen Yüksel Perktaş |
| author_facet | Bilal Eftal Acet Erol Kılıç Selcen Yüksel Perktaş |
| author_sort | Bilal Eftal Acet |
| collection | DOAJ |
| description | We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an η-Einstein manifold. We also investigate some properties of curvature tensor, conformal curvature tensor, W2-curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor with respect to canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to canonical paracontact connection is of constant scalar curvature. We give some characterizations for pseudo-projectively flat para-Sasakian manifolds. |
| format | Article |
| id | doaj-art-7a8eb2eeea3940a887a82f56ec7f1404 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7a8eb2eeea3940a887a82f56ec7f14042025-02-03T05:54:39ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/395462395462Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact ConnectionBilal Eftal Acet0Erol Kılıç1Selcen Yüksel Perktaş2Department of Mathematics, Arts and Science Faculty, Adıyaman University, 02040 Adıyaman, TurkeyDepartment of Mathematics, Arts and Science Faculty, İnönü University, 44280 Malatya, TurkeyDepartment of Mathematics, Arts and Science Faculty, Adıyaman University, 02040 Adıyaman, TurkeyWe study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an η-Einstein manifold. We also investigate some properties of curvature tensor, conformal curvature tensor, W2-curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor with respect to canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to canonical paracontact connection is of constant scalar curvature. We give some characterizations for pseudo-projectively flat para-Sasakian manifolds.http://dx.doi.org/10.1155/2012/395462 |
| spellingShingle | Bilal Eftal Acet Erol Kılıç Selcen Yüksel Perktaş Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection International Journal of Mathematics and Mathematical Sciences |
| title | Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection |
| title_full | Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection |
| title_fullStr | Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection |
| title_full_unstemmed | Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection |
| title_short | Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection |
| title_sort | some curvature conditions on a para sasakian manifold with canonical paracontact connection |
| url | http://dx.doi.org/10.1155/2012/395462 |
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