Some problems on the geometry of calibrated manifolds

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2018

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Yalçınkaya, Eyüp

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In this thesis,w estudy three problems ont he geometry of calibrated manifolds,which are Riemannian manifolds equipped with a special closed differential form called a calibration. Firstly, we compute the homology of Grasmannian manifold of oriented 3-planes in R6, namely G+ 3 (R6), and its special submanifold called SLAG, the set of 3-planes in G+ 3 (R6) determined by the special Lagrangian calibration on CalabiYau 3-fold C3 ∼ = R6. We make an immediate application of these computations. Secondly,weinvestigatearelatedproblemontheembeddingoforientedclosedmanifoldsintoCn asspecialLagrangian-free(sLag-free). Finally,westudythegeography of symplectic 8-dimensional manifolds and obtain certain results on the existence of symplectic 8-manifolds with Spin(7)-structure.

Subject Keywords

Manifolds (Mathematics)., Submanifolds.

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http://etd.lib.metu.edu.tr/upload/12622972/index.pdf
https://hdl.handle.net/11511/27920

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

E. Yalçınkaya, “Some problems on the geometry of calibrated manifolds,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.