Some problems on the geometry of calibrated manifolds

Download

index.pdf

Date

2018

Author

Yalçınkaya, Eyüp

Metadata

Show full item record

Item Usage Stats

137
views

46
downloads

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.

URI

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

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Streamwise oscillations of a cylinder beneath a free surface: Free surface effects on vortex formation modes Bozkaya, Canan; Mironova, L. A.; Gubanov, O. I. (Elsevier BV, 2011-06-15) A computational study of a viscous incompressible two-fluid model with an oscillating cylinder is investigated at a Reynolds number of 200 and at a dimensionless displacement amplitude of A = 0.13 and for the dimensionless forcing cylinder oscillation frequency-to-natural vortex shedding frequency ratios, f/f(0) = 1.5, 2.5, 3.5. Specifically, two-dimensional flow past a circular cylinder subject to forced in-line oscillations beneath a free surface is considered. The method is based on a finite volume discr...
An obstruction to finding algebraic models for smooth manifolds with prescribed algebraic submanifolds CELIKTEN, A; Ozan, Yıldıray (2001-03-01) Let N ⊆ M be a pair of closed smooth manifolds and L an algebraic model for the submanifold N. In this paper, we will give an obstruction to finding an algebraic model X of M so that the submanifold N corresponds in X to an algebraic subvariety isomorphic to L.
Implementation of sensorless vector control drive with current position estimation Filci, Tayfun; Ertan, Hulusi Bülent; Department of Electrical and Electronics Engineering (2016) In this thesis, an algorithm will be developed and implemented online for the estimation of rotor position from the rotor slot harmonics in stator currents. Experiments will be done on an inverter driven induction motor hardware, and the performance of the position detection algorithm will be evaluated in comparison with commercial encoder outputs.
Accurate numerical bounds for the spectral points of singular Sturm-Liouville problems over 0 < x < infinity Taşeli, Hasan (Elsevier BV, 2004-03-01) The eigenvalues of singular Sturm-Liouville problems defined over the semi-infinite positive real axis are examined on a truncated interval 0<x<l as functions of the boundary point l. As a basic theoretical result, it is shown that the eigenvalues of the truncated interval problems satisfying Dirichlet and Neumann boundary conditions provide, respectively, upper and lower bounds to the eigenvalues of the original problem. Moreover, the unperturbed system in a perturbation problem, where l remains sufficient...
On a problem of Osserman in Lorentzian geometry GarciaRio, E; Kupeli, DN; VazquezAbal, ME (Elsevier BV, 1997-03-01) A problem of Osserman on the constancy of the eigenvalues of the Jacobi operator is studied in Lorentzian geometry. Attention is paid to the different cases of timelike, spacelike and null Osserman condition. One also shows a relation between the null Osserman condition and a previous one on infinitesimal null isotropy.

Citation Formats

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