Riemannian submersions from almost contact metric manifolds

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.Comment: Abh. Math. Semin. Univ. Hamb., to appea

On paraquaternionic submersions between paraquaternionic K\"ahler manifolds

In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic K\"ahler non locally hyper paraK\"ahler manifolds. Then we examine, as an example, the canonical projection of the tangent bundle, endowed with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.Comment: 13 pages, no figure

Hidden symmetries and Killing tensors on curved spaces

Higher order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. One presents the infinite dimensional superalgebra of Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be seen as a twisted loop algebra. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed Sasakian structures.Comment: 12 pages; talk presented at Group 27 Colloquium, Yerevan, Armenia, August 200

Hidden Symmetries for Ellipsoid-Solitonic Deformations of Kerr-Sen Black Holes and Quantum Anomalies

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and studied hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.Comment: latex2e, 11pt, 34 pages, the variant accepted by EPJC, with additional explanations, modifications and new references requested by refere

Wave maps from Gödelʼs universe

Using a result by L. Koch we realize G\"ode's universe $\mathcal{G}^4_\alpha = (\mathbb{R}^4, g_\alpha )$ as the total space of a principal $\mathbb{R}$-bundle over a strictly pseudoconvex CR manifold $M^3$ and exploit the analogy between $g_\alpha$ and Fefferman's metric $F_\theta$ to show that for any $\mathbb{R}$-invariant wave map $\Phi$ of $\mathcal{G}^4_\alpha$ into a Riemannian manifold $N$, the corresponding base map $\phi : M^3 \to N$ is subelliptic harmonic, with respect to a canonical choice of contact form $\theta$ on $M^3$. We show that the subelliptic Jacobi operator $J^\phi_b$ of $\phi$ has a discrete Dirichlet spectrum on any bounded domain $D \subset M^3$ supporting the Poincar\'e inequality on \IN{W}^{1,2}_H (D, \phi^{-1} T N) and Kondrakov compactness i.e. compactness of the embedding \IN{W}^{1,2}_H (D, \phi^{-1} T N) \hookrightarrow L^2 (D, \phi^{-1} T N). We exhibit an explicit solution $\pi:\mathcal{G}^4_\alpha \to M^3$ to the wave map system on $\mathcal{G}^4_\alpha$, of index $\mathrm{ind}^\Omega (\pi ) \geq 1$ for any bounded domain $\Omega \subset \mathcal{G}^4_\alpha$. Mounoud's distance $d^\infty_{G_0, \Omega} (g_\alpha, F_\theta )$ is bounded below by a constant depending only on the rotation frequency of G\"odel's universe, thus giving a measure of the bias of $g_\alpha$ from being Fefferman like in the region $\Omega \subset \mathbb{R}^4$

Relevance of time-dependence for clinically viable diffusion imaging of the spinal cord

10.1002/mrm.27463Magnetic Resonance in Medicin