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We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures. [ABSTRACT FROM AUTHOR]

The Gauss map of a projective variety X ⊂ PN is a rational map from X to a Grassmann variety. In positive characteristic, we show the following results. (1) For given projective varieties F and Y, we construct a projective variety X whose Gauss map has F as its general fiber and has Y as its image. More generally, we give such construction for families of varieties over Y instead of fixed F. (2) At least in the case when the characteristic is not equal to 2, any inseparable field extension appears as the extension induced from the Gauss map of some X. [ABSTRACT FROM AUTHOR]

Let G be a connected complex Lie group or a connected amenable Lie group. We show that any flat principal G-bundle over any finite CW-complex pulls back to a trivial G-bundle over some finite covering space of the base space if and only if the derived group of the radical of G is simply connected. In particular, if G is a connected compact Lie group or a connected complex reductive Lie group, then any flat principal G-bundle over any finite CW-complex pulls back to a trivial G-bundle over some finite covering space of the base space. [ABSTRACT FROM AUTHOR]

We prove the cyclic formality conjecture for chains, raised by Tsygan [“Formality conjectures for chains.” Differential Topology, Infinite-dimensional Lie Algebras, and Applications 261–74. American Mathematical Society Translation Series 2, 194. Providence, RI: American Mathematical Society, 1999.]. It states the existence of an L∞-quasi-isomorphism of L∞-modules between the cyclic chain complex of smooth functions on a manifold and the differential forms on that manifold. Concretely, we prove that the u-linear extension of Shoikhet’s morphism of Hochschild chains [Shoikhet, B. “A proof of the Tsygan formality conjecture for chains.” Advances in Mathematics 179, no. 1 (2003): 7–37.] solves Tsygan’s conjecture. [ABSTRACT FROM PUBLISHER]

To achieve better precision in describing contaminant dispersion in channels some authors resort to dividing a channel into two zones, fast and slow, leading to a pair of coupled evolution equations for cross‐sectionally‐averaged concentrations in the zones. We construct a two‐zone model whose accuracy is guaranteed by centre manifold theory. The model leads to evolution equations that differ from existing models. We also formulate modified initial conditions for the model to obtain closer correlation between the manifold solution and real solution. Effectiveness of the modified initial conditions is demonstrated numerically by a comparison between the manifold solution and direct numerical simulations of the original advection–diffusion equations. [ABSTRACT FROM PUBLISHER]

If T is an R‐tree and Γ is a group of isometries acting properly discontinuously on T, it is shown that the geodesic flow on the quotient metric space X = T/Γ, when restricted to the non‐wandering set, is topologically mixing if and only if the lengths of the closed geodesics in X generate a dense subset of R. [ABSTRACT FROM PUBLISHER]

We prove some boundary rigidity theorems for a compact Riemannian manifold with boundary and non‐negative Ricci curvature. [ABSTRACT FROM PUBLISHER]

The article presents a study on the manifold of bundle-like metrics of a Riemannian foliation. It examines metric sections of a vector bundle compared with an unnecessary compact manifold which is smooth sections of a bundle of positive definite symmetric bilinear forms. It explores the geometry of the manifold with regards to the manifold of metric sections and the manifolds related to a vector bundle.

The article presents the solution to the mathematical problem of estimates for weighted volumes and applications. It states that the Reimannian manifold was used to derive weighted volume measures which is a product of the study on conformal deformation of a Reimannain metric. It explores the concept of curvature related to a weighted Laplacian and provides proof of theorems used in weighted volume measures.

In [11], two of us constructed a closed oriented 4-dimensional manifold with fundamental group ℤ that does not split off S1 × S3. In this note we show that this 4-manifold, and various others derived from it, do not admit smooth structures. Moreover, we find an infinite family of 4-manifolds with exactly the same properties. As a corollary, we obtain topologically slice knots that are not smoothly slice in any rational homology ball. [ABSTRACT FROM PUBLISHER]

The article focuses on Ramanujan type congruences. The authors explain that the Ramanujan 691 congruence is related to the special value of the Rankin-Selzberg zeta function. They present the approach they used which leads to many congruences. They also mention that in Jacobi forms, one can find single congruences.