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Annals of Global Analysis and Geometry

, Volume 43, Issue 2, pp 123–141 | Cite as

Lee form and special warped-like product manifolds with locally conformally parallel Spin(7) structure

  • Selman Uğuz
Article

Abstract

We study the cases of the Lee form on special warped-like product manifolds M with locally conformally parallel Spin(7) structure to determine the nature of the fibers. Using fiber-base decomposition, we prove that the connection on M is determined by the Bonan form and Lee one-form. Assuming that the fibers are complete, connected and simply connected, and choosing some classes of Lee form on M, we prove a main result that the fibers (or at least one of them) are isometric to S 3 with constant curvature k > 0 in the class of (3 + 3 + 2) warped-like product metrics admitting a specific locally conformally parallel Spin(7) structure. We believe that the paper could help in producing new examples of (locally conformally) parallel Spin(7) structures.

Keywords

Lee form Holonomy Locally conformally parallel Spin(7) manifold Warped product Multiply-warped product (3 + 3 + 2) Warped-like product 

Mathematics Subject Classification

53C25 53C29 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsHarran UniversityŞanliurfaTurkey

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