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References [1] Bryant, R., Salamon, S., On the Construction of Some Complete Metrics with Exceptional Holonomy, Duke Mathematical Journal (3) 58 (1989) 829-850. [2] Fern´andez, M. and Gray, A., Riemannian manifolds with structure group G 2, Ann. Mat. Pura Appl. (4) 132 (1982) 19-25. [3] Friedrich, T., Dirac Operators in Riemannian Geometry, American Mathematical Society, Providence, 2000. [4] Hijazi, O., Spectral Properties of the Dirac operator and geometrical structures, Proceedings of the Summer School on Geometric Methods in Quantum Field Theory, Villa de

References [1] J. A. Alvarez Lopez, The basic component of the mean curvature of Riemannian foliations, Ann. Global Anal. Geom. 10 (1992), 179-194. [2] J. A. Alvarez Lopez, Y.A. Kordyukov, Adiabatic limits and spectral sequences for Riemannian foliations, Geom. and Funct. Anal. 10 (2000), 977-1027. [3] J. Brüning, F.W. Kamber, Vanishing theorems and index formulas for transversal Dirac operators, AMS Meeting 845, Special Session on Op- erator Theory and Applications to Geometry, American Mathematical Society Abstracts, Lawrence, KA, 1988. [4] M. Craioveanu, M

References [1] Akbulut S., Lecture Notes on Seiberg-Witten Invariants , Turkish Journal of Mathematics, 20 (1996), 95-118. [2] Davidov J., Grantcharov G., Mushkarov O., Geometry of Neutral Metricin Dimension Four , arXiv:0804.2132v1. [3] Değirmenci N., Özdemir N., Seiberg-Witten Equations on Lorentzianspinc manifolds , International Journal of Geometric Methods in Modern Physics, 8(4) , 2011. [4] Dunajki, M., West, S., Anti-Self-Dual Conformal Structures in NeutralSignature , arXiv.math/0610280v4. [5] Friedrich T., Dirac Operators in Riemannian Geometry


We identify a class of magnetic Schrödinger operators on Käler manifolds which exhibit pure point spectrum. To this end we embed the Schröinger problem into a Dirac-type problem via a parallel spinor and use a Bochner-Weitzenböck argument to prove our spectral discreteness criterion

References [1] I. Agricola, A.C. Ferreira: Einstein manifolds with skew torsion. Oxford Quart. J. (65) (2014) 717–741. [2] I. Agricola, Th. Friedrich: On the holonomy of connections with skew-symmetric torsion. Math. Ann. (328) (2004) 711–748. [3] I. Agricola, J. Becker-Bender, H. Kim: Twistorial eigenvalue estimates for generalized Dirac operators with torsion. Adv. Math. (243) (2013) 296–329. [4] B. Ammann, C. Bär: The Einstein-Hilbert action as a spectral action. Noncommutative Geometry and the Standard Model of Elementary Particle Physics (2002) 75

), 743 - 755. [4] B.P. Allahverdiev, Spectral analysis of dissipative Dirac operators with general boundary conditions, J. Math. Anal. Appl. 283 (2003), 287 - 303. [5] B.P. Allahverdiev, Dilation and Functional Model of Dissipative Operator Generated by an Infinite Jacobi Matrix, Math. and Comp. Modelling 38, 3 (2003), 989 - 1001. [6] M. Baro, H. Neidhardt Dissipative Schrodinger-type operators as a model for generation and recombination, J. Math. Phys. 44, 6 (2003), 2373 - 2401. [7] M. Baro, H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Dissipative Schrödinger

proof of the expansion theorem for singular second order linear differential equations. Duke Math. J. 18 (1951) 57–71. [30] B.M. Levitan, I.S. Sargsjan: Sturm-Liouville and Dirac Operators . Springer (1991). [31] M.A. Naimark: Linear Differential Operators, 2nd edn., 1968 . Nauka, Moscow (1969). English translation of 1st edn. [32] J. Petronilho: Generic formulas for the values at the singular points of some special monic classical H q,ω -orthogonal polynomials.. J. Comput. Appl. Math. 205 (2007) 314–324. [33] T. Sitthiwirattham: On a nonlocal boundary value

transform, Communication Theoretical Physics 39 (1): 97-100. Hong-yi, F. and Zaidi, H. (1987). New approach for calculating the normally ordered form of squeeze operators, Physical Review D 35 (6): 1831-1834. Hua, J., Liu, L. and Li, G. (1997). Extended fractional Fourier transforms, Journal of Optical Society of America A 14 (12): 3316-3322. Huang, J. and Pandić, P. (2006). Dirac Operators in Representation Theory , Birkhauser/Springer, Boston, MA/ New York, NY. James, D. and Agarwal, G. (1996). The generalized Fresnel transform and its applications to optics