Bochner and conformal flatness of normal metric contact pairs

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• 作者：Gianluca Bande ; David E. Blair ; Amine Hadjar
• 关键词：Normal metric contact pairs ; Bochner ; flat ; Locally conformally flat ; Vaisman manifolds
• 刊名：Annals of Global Analysis and Geometry
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：48
• 期：1
• 页码：47-56
• 全文大小：387 KB
• 参考文献：1.Bande, G., Hadjar, A.: Contact pair structures and associated metrics. In: Differential Geometry—Proceedings of the 8th International Colloquium, pp. 266-75. World Sci. Publ., Hackensack, NJ (2009)
  2.Bande, G., Hadjar, A.: Minimality of invariant submanifolds in metric contact pair geometry. Ann. Mat. Pura Appl. doi:10.-007/?s10231-014-0412-8 (to appear)
  3.Bande, G., Hadjar, A.: On the characteristic foliations of metric contact pairs. In: Harmonic Maps and Differential Geometry. Contemp. Math., vol. 542, pp. 255-59. American Mathematical Society, Providence (2011)
  4.Bande, G., Kotschick, D.: Contact pairs and locally conformally symplectic structures. In: Harmonic Maps and Differential geometry. Contemp. Math., vol. 542, pp. 85-8. American Mathematical Society, Providence (2011)
  5.Bande, G.: Formes de Contact Généralisé, Couples de Contact et Couples Contacto-symplectiques, Thèse de Doctorat. Université de Haute Alsace, Mulhouse (2000)
  6.Bande, G., Hadjar, A.: Contact pairs. T?hoku Math. J. 57, 247-60 (2005)View Article MATH MathSciNet
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  12.Blair, D.E., Martín-Molina, V.: Bochner and conformal flatness on normal complex contact metric manifolds. Ann. Glob. Anal. Geom. 39, 249-58 (2011)View Article MATH
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  14.Kashiwada, T.: On locally conformal K?hler structures. In: New Developments in Differential Geometry (Debrecen, 1994). Math. Appl., vol. 350, pp. 225-31. Kluwer, Dordrecht (1996)
  15.Korkmaz, B.: Normality of complex contact manifolds. Rocky Mt. J. Math. 30, 1343-380 (2000)View Article MATH MathSciNet
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  18.Yano, K.: Differential Geometry on Complex and Almost Complex Spaces. Pergamon Press, Oxford (1964)
  
• 作者单位：Gianluca Bande (1)
  David E. Blair (2)
  Amine Hadjar (3)
  
  1. Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy
  2. Department of Mathematics, Michigan State University, East Lansing, MI, 48824-1027, USA
  3. Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, 4, Rue des Frères Lumière, 68093, Mulhouse Cédex, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Mathematical and Computational Physics
  Group Theory and Generalizations
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9060

文摘

We prove that the normal metric contact pairs with orthogonal characteristic foliations, which are either Bochner-flat or locally conformally flat, are locally isometric to the Hopf manifolds. As a corollary we obtain the classification of locally conformally flat and Bochner-flat non-K?hler Vaisman manifolds.