查看更多>>摘要：Applying the point of view of non-holonomic mechanics, we arrive at a new and simple system of equations for the normal sub-Riemannian geodesics. These use a partial connection that is canonically available, given a choice of complement to the distribution. We also describe conditions which, if satisfied, mean that even this choice of complement is determined canonically, and that this determines a distinguished connection on the tangent bundle. The geodesic equations obtained split into mutually driving horizontal and complementary parts. The method facilitates efficient choices of adapted coframes and reveals structures that are reminiscent of tractor calculi. We illustrate the features on examples, including some with non-constant symbols. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We define certain extensions of Jacobi groups of A(n), prove an analogue of Chevalley Theorem for their invariants and construct a Dubrovin Frobenius structure on its orbit space. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The zeroth line bundle cohomology on Calabi-Yau three-folds encodes information about the existence of flop transitions and the genus zero Gromov-Witten invariants. We illustrate this claim by studying several Picard number 2 Calabi-Yau three-folds realised as complete intersections in products of projective spaces. Many of these manifolds exhibit certain symmetries on the Picard lattice which preserve the zeroth cohomology. (c) 2021 Published by Elsevier B.V.
查看更多>>摘要：We construct a metric structure on a configuration space of gauge connections and show that it naturally produces a candidate for a non-perturbative, 3+1 dimensional YangMills-Dirac quantum field theory on a curved background. The metric structure is an infinite-dimensional Bott-Dirac operator and the fermionic sector of the emerging quantum field theory is generated by the infinite-dimensional Clifford algebra required to construct this operator. The Bott-Dirac operator interacts with the HD(M) algebra, which is a noncommutative algebra generated by holonomy-diffeomorphisms on the underlying manifold, i.e. parallel-transforms along flows of vector fields. This algebra combined with the BottDirac operator encode the canonical commutation and anti-commutation relations of the quantised bosonic and fermionic fields. The square of the Bott-Dirac operator produces both the Yang-Mills Hamilton operator and the Dirac Hamilton operator as well as a topological Yang-Mills term alongside higher-derivative terms and a metric invariant. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Using the technique of pedal coordinates we investigate the orbits of a free double linkage. We provide a geometrical construction for them and also show a surprising connection between this mechanical system and orbits around a Black Hole and solutions of Dark Kepler problem. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We obtain a classification result for rotational surfaces in Berger spheres, whose mean curvature is given as a prescribed function of their angle function. Under hypothesis on the prescribed function, we show that these surfaces behave like the Delaunay surfaces of constant mean curvature. The classification is done by means of a phase plane analysis of the ODE fulfilled by the profile curve of such surfaces. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We introduce analogs of creation and annihilation operators, related to involutive and Hecke symmetries R, and perform bosonic and fermionic realization of the modified Reflection Equation algebras in terms of the so-called Quantum Doubles of Fock type. Also, we introduce Quantum Doubles of Fock type, associated with Birman-Murakami-Wenzl symmetries coming from orthogonal or simplectic Quantum Groups and exhibit the algebras obtained by means of the corresponding bosonization (fermionization). Besides, we apply this scheme to current braidings arising from Hecke symmetries R via the Baxterization procedure. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We study the monodromy of the Hitchin fibration for moduli spaces of parabolic G-Higgs bundles in the cases when G = SL(2, R), GL(2, R) and PGL(2, R). A calculation of the orbits of the monodromy with Z(2)-coefficients provides an exact count of the components of the moduli spaces for these groups. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Using a combinatorial description of Stiefel-Whitney classes of closed flat manifolds with diagonal holonomy representation, we show that no Hantzsche-Wendt manifold of dimension greater than three admits a spin(c) structure. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
查看更多>>摘要：In Lee et al. (2020) [21], the authors of the present article proved two optimal inequalities delta(C)(n - 1) and (delta(C)) over cap (n - 1) of n-dimensional Legendrian submanifolds in Sasakian space forms and identified the classes of those submanifolds for which the equality cases of both inequalities hold. The aim of this paper is to generalize these results to the case of generalized Casorati curvatures delta(C)(r; n - 1) and (delta(C)) over cap (r; n - 1), which are fundamental extrinsic invariants of Riemannian submanifolds originally introduced by Decu et al. (2008) [14] as a natural generalization of delta(C)(n - 1) and (delta(C)) over cap (n - 1), where ris any real number such that 0 < r < n(n - 1) or r > n(n - 1), respectively. We also provide examples of submanifolds that are ideal for any given r. (c) 2021 Elsevier B.V. All rights reserved.
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