# Dancing Mathematics and the Mathematics of Dance

## Related Articles

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In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In particular, we show that each symmetric conformal geometry...

- On KÃ¤hler conformal compactifications of U( n)-invariant ALE spaces. Dabkowski, Michael; Lock, Michael // Annals of Global Analysis & Geometry;Jan2016, Vol. 49 Issue 1, p73
We prove that a certain class of asymptotically locally Euclidean spaces always has a KÃ¤hler conformal compactification, and moreover provide explicit formulas for the conformal factor and the KÃ¤hler potential of said compactification. We then apply this to give a new and simple...

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We prove that for each partition of the Lobachevsky plane into finitely many Borel pieces one of the cells of the partition contains an unbounded centrally symmetric subset.

- Topology identification of complex dynamical networks. Junchan Zhao; Qin Li; Jun-An Lu; Zhong-Ping Jiang // Chaos;Jun2010, Vol. 20 Issue 2, p023119
Recently, some researchers investigated the topology identification for complex networks via LaSalleâ€™s invariance principle. The principle cannot be directly applied to time-varying systems since the positive limit sets are generally not invariant. In this paper, we study the topology...

- Lie jets and symmetries of prolongations of geometric objects. Shurygin, V. // Journal of Mathematical Sciences;Sep2011, Vol. 177 Issue 5, p758
The Lie jet LÎ» of a field of geometric objects Î» on a smooth manifold M with respect to a field Î¸ of Weil A-velocities is a generalization of the Lie derivative LÎ» of a field Î» with respect to a vector field v. In this paper, Lie jets LÎ» are applied to the study of A-smooth...

- Finite-Time Blowup in a Supercritical Quasilinear Parabolic-Parabolic Keller-Segel System in Dimension 2. Cieślak, Tomasz; Stinner, Christian // Acta Applicandae Mathematica;Feb2014, Vol. 129 Issue 1, p135
In this note we show finite-time blowup of radially symmetric solutions to the quasilinear parabolic-parabolic two-dimensional Keller-Segel system for any positive mass. We prove this result by slightly adapting M. Winkler's method, which he introduced in (Winkler in J. Math. Pures Appl., , )...

- A triplectic bi-Darboux theorem and para-hypercomplex geometry. Batalin, Igor A.; Bering, Klaus // Journal of Mathematical Physics;Dec2012, Vol. 53 Issue 12, p123507
We provide necessary and sufficient conditions for a bi-Darboux theorem on triplectic manifolds. Here, triplectic manifolds are manifolds equipped with two compatible, jointly non-degenerate Poisson brackets with mutually involutive Casimirs, and with ranks equal to 2/3 of the manifold...

- A Note On The Quasi-Conformal And M-Projective Curvature Tensor Of A Semi-Symmetric Recurrent Metric Connection On A Riemannian Manifold. Kumar, Rajesh; Chowdhury, Jagannath // Suleyman Demirel University Journal of Science;2013, Vol. 8 Issue 2, p190
In the present note we have considered Mn to be a Riemannian manifold admitting a semi-symmetric recurrent metric connection. The aim of the present paper is to obtain the conditions under which the quasi-conformal curvature tensor and M-projective curvature tensor of semi-symmetric recurrent...

- CONFORMALLY FLAT LORENTZIAN THREE-SPACES WITH VARIOUS PROPERTIES OF SYMMETRY AND HOMOGENEITY. CALVARUSO, GIOVANNI // Archivum Mathematicum;2010, Vol. 46 Issue 2, p119
We study conformally flat Lorentzian three-manifolds which are either semi-symmetric or pseudo-symmetric. Their complete classification is obtained under hypotheses of local homogeneity and curvature homogeneity. Moreover, examples which are not curvature homogeneous are described.