Contact Metric Spaces and pseudo-Hermitian Symmetry
We prove that a contact strongly pseudo-convex CR (Cauchy–Riemann) manifold <inline-formula><math display="inline"><semantics><msup><mi>M</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/9/1583 |
| _version_ | 1797553771981570048 |
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| author | Jong Taek Cho |
| author_facet | Jong Taek Cho |
| author_sort | Jong Taek Cho |
| collection | DOAJ |
| description | We prove that a contact strongly pseudo-convex CR (Cauchy–Riemann) manifold <inline-formula><math display="inline"><semantics><msup><mi>M</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>, is locally pseudo-Hermitian symmetric and satisfies <inline-formula><math display="inline"><semantics><mrow><msub><mo>∇</mo><mi>ξ</mi></msub><mi>h</mi><mo>=</mo><mi>μ</mi><mi>h</mi><mi>ϕ</mi></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><mi>μ</mi><mo>∈</mo><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>, if and only if <i>M</i> is either a Sasakian locally <inline-formula><math display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-symmetric space or a non-Sasakian <inline-formula><math display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>k</mi><mo>,</mo><mi>μ</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>-space. When <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, we prove a classification theorem of contact strongly pseudo-convex CR manifolds with pseudo-Hermitian symmetry. |
| first_indexed | 2024-03-10T16:21:22Z |
| format | Article |
| id | doaj.art-3fbf293a58474afebd24fa2cc7d81b88 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T16:21:22Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3fbf293a58474afebd24fa2cc7d81b882023-11-20T13:38:33ZengMDPI AGMathematics2227-73902020-09-0189158310.3390/math8091583Contact Metric Spaces and pseudo-Hermitian SymmetryJong Taek Cho0Department of Mathematics, Chonnam National University, Gwangju 61186, KoreaWe prove that a contact strongly pseudo-convex CR (Cauchy–Riemann) manifold <inline-formula><math display="inline"><semantics><msup><mi>M</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>, is locally pseudo-Hermitian symmetric and satisfies <inline-formula><math display="inline"><semantics><mrow><msub><mo>∇</mo><mi>ξ</mi></msub><mi>h</mi><mo>=</mo><mi>μ</mi><mi>h</mi><mi>ϕ</mi></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><mi>μ</mi><mo>∈</mo><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>, if and only if <i>M</i> is either a Sasakian locally <inline-formula><math display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-symmetric space or a non-Sasakian <inline-formula><math display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>k</mi><mo>,</mo><mi>μ</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>-space. When <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, we prove a classification theorem of contact strongly pseudo-convex CR manifolds with pseudo-Hermitian symmetry.https://www.mdpi.com/2227-7390/8/9/1583contact almost CR (Cauchy–Riemann) manifoldgeneralized Tanaka-Webster connectionpseudo-Hermitian symmetric space |
| spellingShingle | Jong Taek Cho Contact Metric Spaces and pseudo-Hermitian Symmetry Mathematics contact almost CR (Cauchy–Riemann) manifold generalized Tanaka-Webster connection pseudo-Hermitian symmetric space |
| title | Contact Metric Spaces and pseudo-Hermitian Symmetry |
| title_full | Contact Metric Spaces and pseudo-Hermitian Symmetry |
| title_fullStr | Contact Metric Spaces and pseudo-Hermitian Symmetry |
| title_full_unstemmed | Contact Metric Spaces and pseudo-Hermitian Symmetry |
| title_short | Contact Metric Spaces and pseudo-Hermitian Symmetry |
| title_sort | contact metric spaces and pseudo hermitian symmetry |
| topic | contact almost CR (Cauchy–Riemann) manifold generalized Tanaka-Webster connection pseudo-Hermitian symmetric space |
| url | https://www.mdpi.com/2227-7390/8/9/1583 |
| work_keys_str_mv | AT jongtaekcho contactmetricspacesandpseudohermitiansymmetry |