Lee form and special warped-like product manifolds with locally conformally parallel Spin(7) structure
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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.
KeywordsLee form Holonomy Locally conformally parallel Spin(7) manifold Warped product Multiply-warped product (3 + 3 + 2) Warped-like product
Mathematics Subject Classification53C25 53C29
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