Reducibility in Sasakian Geometry
| Autor: | Charles P. Boyer, Christina W. Tønnesen-Friedman, Eveline Legendre, Hongnian Huang |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
General Mathematics [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Geometry Type (model theory) 01 natural sciences 53C25 symbols.namesake Genus (mathematics) 0103 physical sciences FOS: Mathematics 0101 mathematics Mathematics::Symplectic Geometry decomposable Mathematics Applied Mathematics Riemann surface Sasakian 010102 general mathematics Zero (complex analysis) Algebraic variety Join (topology) join Cone (topology) Differential Geometry (math.DG) reducible Isotopy symbols 010307 mathematical physics Mathematics::Differential Geometry |
| Zdroj: | Trans.Am.Math.Soc. Trans.Am.Math.Soc., 2018, 370 (10), pp.6825-6869. ⟨10.1090/tran/7526⟩ |
| DOI: | 10.1090/tran/7526⟩ |
| Popis: | The purpose of this paper is to study reducibility properties in Sasakian geometry. First we give the Sasaki version of the de Rham Decomposition Theorem; however, we need a mild technical assumption on the Sasaki automorphism group which includes the toric case. Next we introduce the concept of {\it cone reducible} and consider $S^3$ bundles over a smooth projective algebraic variety where we give a classification result concerning contact structures admitting the action of a 2-torus of Reeb type. In particular, we can classify all such Sasakian structures up to contact isotopy on $S^3$ bundles over a Riemann surface of genus greater than zero. Finally, we show that in the toric case an extremal Sasaki metric on a Sasaki join always splits. Comment: 58 pages, minor corrections made in latest version; a reference added and references updated; to appear in the Transactions of the American Mathematical Society |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|