Transversal Jacobi Operators in Almost Contact Manifolds
Along a transversal geodesic <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> whose tangent belongs to the contact distribution <i>D</i>, we define the transversal Jacobi operator &l...
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MDPI AG
2020-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/1/31 |
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| author | Jong Taek Cho Makoto Kimura |
| author_facet | Jong Taek Cho Makoto Kimura |
| author_sort | Jong Taek Cho |
| collection | DOAJ |
| description | Along a transversal geodesic <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> whose tangent belongs to the contact distribution <i>D</i>, we define the transversal Jacobi operator <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>γ</mi></msub><mo>=</mo><mi>R</mi><mrow><mo>(</mo><mo>·</mo><mo>,</mo><mover accent="true"><mi>γ</mi><mo>˙</mo></mover><mo>)</mo></mrow><mover accent="true"><mi>γ</mi><mo>˙</mo></mover></mrow></semantics></math></inline-formula> on an almost contact Riemannian manifold <i>M</i>. Then, using the transversal Jacobi operator <inline-formula><math display="inline"><semantics><msub><mi>R</mi><mi>γ</mi></msub></semantics></math></inline-formula>, we give a new characterization of the Sasakian sphere. In the second part, we characterize the complete ruled real hypersurfaces in complex hyperbolic space. |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T13:47:40Z |
| publishDate | 2020-12-01 |
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| spelling | doaj.art-953b4d1c4fee4dc590331ce3404c4cc82023-11-21T02:27:16ZengMDPI AGMathematics2227-73902020-12-01913110.3390/math9010031Transversal Jacobi Operators in Almost Contact ManifoldsJong Taek Cho0Makoto Kimura1Department of Mathematics, Chonnam National University, Gwangju 61186, KoreaDepartment of Mathematics, Faculty of Science, Ibaraki University, Mito, Ibaraki 310-8512, JapanAlong a transversal geodesic <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> whose tangent belongs to the contact distribution <i>D</i>, we define the transversal Jacobi operator <inline-formula><math display="inline"><semantics><mrow><msub><mi>R</mi><mi>γ</mi></msub><mo>=</mo><mi>R</mi><mrow><mo>(</mo><mo>·</mo><mo>,</mo><mover accent="true"><mi>γ</mi><mo>˙</mo></mover><mo>)</mo></mrow><mover accent="true"><mi>γ</mi><mo>˙</mo></mover></mrow></semantics></math></inline-formula> on an almost contact Riemannian manifold <i>M</i>. Then, using the transversal Jacobi operator <inline-formula><math display="inline"><semantics><msub><mi>R</mi><mi>γ</mi></msub></semantics></math></inline-formula>, we give a new characterization of the Sasakian sphere. In the second part, we characterize the complete ruled real hypersurfaces in complex hyperbolic space.https://www.mdpi.com/2227-7390/9/1/31almost contact manifoldtransversal Jacobi operatorSasakian sphereruled real hypersurface |
| spellingShingle | Jong Taek Cho Makoto Kimura Transversal Jacobi Operators in Almost Contact Manifolds Mathematics almost contact manifold transversal Jacobi operator Sasakian sphere ruled real hypersurface |
| title | Transversal Jacobi Operators in Almost Contact Manifolds |
| title_full | Transversal Jacobi Operators in Almost Contact Manifolds |
| title_fullStr | Transversal Jacobi Operators in Almost Contact Manifolds |
| title_full_unstemmed | Transversal Jacobi Operators in Almost Contact Manifolds |
| title_short | Transversal Jacobi Operators in Almost Contact Manifolds |
| title_sort | transversal jacobi operators in almost contact manifolds |
| topic | almost contact manifold transversal Jacobi operator Sasakian sphere ruled real hypersurface |
| url | https://www.mdpi.com/2227-7390/9/1/31 |
| work_keys_str_mv | AT jongtaekcho transversaljacobioperatorsinalmostcontactmanifolds AT makotokimura transversaljacobioperatorsinalmostcontactmanifolds |