The Scalar Curvature of a Riemannian Almost Paracomplex Manifold and Its Conformal Transformations
A Riemannian almost paracomplex manifold is a 2<i>n</i>-dimensional Riemannian manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>M</mi><mo>,&l...
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1379 |
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| author | Vladimir Rovenski Josef Mikeš Sergey Stepanov |
| author_facet | Vladimir Rovenski Josef Mikeš Sergey Stepanov |
| author_sort | Vladimir Rovenski |
| collection | DOAJ |
| description | A Riemannian almost paracomplex manifold is a 2<i>n</i>-dimensional Riemannian manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></mrow></semantics></math></inline-formula>, whose structural group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></semantics></math></inline-formula> is reduced to the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo><mo>×</mo><mi>O</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></semantics></math></inline-formula>. We define the scalar curvature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> of this manifold and consider relationships between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> and the scalar curvature <i>s</i> of the metric <i>g</i> and its conformal transformations. |
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| language | English |
| last_indexed | 2024-03-10T10:25:55Z |
| publishDate | 2021-06-01 |
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| series | Mathematics |
| spelling | doaj.art-f4b611ed00114b3893d76a55782f4f862023-11-22T00:04:10ZengMDPI AGMathematics2227-73902021-06-01912137910.3390/math9121379The Scalar Curvature of a Riemannian Almost Paracomplex Manifold and Its Conformal TransformationsVladimir Rovenski0Josef Mikeš1Sergey Stepanov2Department of Mathematics, University of Haifa, Mount Carmel, Haifa 3498838, IsraelDepartment of Algebra and Geometry, Palacky University, 77146 Olomouc, Czech RepublicDepartment of Mathematics, Finance University, 49-55, Leningradsky Prospect, 125468 Moscow, RussiaA Riemannian almost paracomplex manifold is a 2<i>n</i>-dimensional Riemannian manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></mrow></semantics></math></inline-formula>, whose structural group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></semantics></math></inline-formula> is reduced to the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo><mo>×</mo><mi>O</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></semantics></math></inline-formula>. We define the scalar curvature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> of this manifold and consider relationships between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> and the scalar curvature <i>s</i> of the metric <i>g</i> and its conformal transformations.https://www.mdpi.com/2227-7390/9/12/1379almost paracomplex manifoldconformal transformationscalar curvature |
| spellingShingle | Vladimir Rovenski Josef Mikeš Sergey Stepanov The Scalar Curvature of a Riemannian Almost Paracomplex Manifold and Its Conformal Transformations Mathematics almost paracomplex manifold conformal transformation scalar curvature |
| title | The Scalar Curvature of a Riemannian Almost Paracomplex Manifold and Its Conformal Transformations |
| title_full | The Scalar Curvature of a Riemannian Almost Paracomplex Manifold and Its Conformal Transformations |
| title_fullStr | The Scalar Curvature of a Riemannian Almost Paracomplex Manifold and Its Conformal Transformations |
| title_full_unstemmed | The Scalar Curvature of a Riemannian Almost Paracomplex Manifold and Its Conformal Transformations |
| title_short | The Scalar Curvature of a Riemannian Almost Paracomplex Manifold and Its Conformal Transformations |
| title_sort | scalar curvature of a riemannian almost paracomplex manifold and its conformal transformations |
| topic | almost paracomplex manifold conformal transformation scalar curvature |
| url | https://www.mdpi.com/2227-7390/9/12/1379 |
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