查看更多>>摘要：This paper is devoted to the geometry of pseudo null curve in terms of anholonomic coordinates in Minkowski space. Firstly, extended Frenet formulas for pseudo null curves are deeply discussed. Then binormal congruence of degenerate surfaces containing the s - lines and n - lines are investigated with the condition mu(b) = 0. This condition represents the necessary and sufficient condition for the existence of a one-parameter family of surfaces containing the s - lines and n - lines. Moreover, normal congruence of surfaces containing the s - lines and b - lines are examined with the condition mu(n) = 0. Again, the condition represents the necessary and sufficient condition for the existence of a one-parameter family of surfaces containing the s - lines and b - lines. Considering the compatibility conditions, Gauss-Mainardi-Codazzi equations are obtained for this binormal and congruence of surfaces, respectively. Finally, some relations are given for constructing the moving pseudo null curve with using the integrable Landau-Lifshitz equation. (C) 2022 Elsevier B.V. All rights reserved.
Refice, AhmedInc, MustafaHashemi, Mir SajjadSouid, Mohammed Said...
13页
查看更多>>摘要：This manuscript deals with the existence, uniqueness and stability of solutions to the boundary value problem (BVP) of Riemann-Liouville (RL) fractional differential equations (FDEs) in the variable exponent Lebesgue spaces (Lp(.)). The generalized intervals and piece-wise constant functions are utilized to extract the aims of current paper. The variable exponent Lebesgue spaces (Lp(.)) are converted to the classical Lebesgue spaces. Further, the Banach contraction principle is used, the Ulam-Hyers-stability is examined and finally, an illustrative example is given to the validity of the observed results. (c) 2022 Elsevier B.V. All rights reserved.
Younas, UsmanSulaiman, T. A.Ren, JingliYusuf, A....
10页
查看更多>>摘要：In this manuscript, we discuss the dynamical behavior of ill-posed Boussinesq (IPB) dynamical wave equation. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The different wave structures are extracted by the utilization of Hirota's bilinear method (HBM) and different test function approaches. The wave structures in the forms of novel breather waves, lump solutions, two-wave solutions, and rogue wave solutions are obtained. Furthermore, with assistance of appropriate parameters, the acquired solutions' physical behavior is drawn out in 3 dimensional, and contour profiles. As a consequence of the obtained results, we can claim that the used methodology is simple, dynamic, extremely effective, and will serve as a useful tool for solving more severely nonlinear problems in a variety of domains, most notably ocean and coastal engineering. Additionally, our findings provide an important first step in comprehending the structure and physical behavior of complex structures. We hope that our findings will contribute significantly to our understanding of ocean waves. This work, we believe, is timely and will be of interest to a broad range of professionals involved in ocean engineering models. The obtained results are useful in grasping the fundamental scenarios of nonlinear sciences. With the help of Mathematica, the obtained results are verified by inserting them into the governing equation. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：A rigidity result for a class of compact generalized quasi-Einstein manifolds with constant scalar curvature is obtained. Moreover, under some geometric assumptions, the rigidity for the non-compact case is also proved. Considering non constant scalar curvature, we characterize the generalized quasi-Einstein manifolds which is conformal to the Euclidean space and we show that there exist two classes of complete manifolds, which are obtained by considering potential functions and conformal factors either to be radial or invariant under the action of an (n-1) dimensional translation group. Explicit examples are given. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We formulate a correspondence between SU(2) monopole chains and "spectral data ", consisting of curves in CP1 x CP1 equipped with parabolic line bundles. This is the analogue for monopole chains of Donaldson's association of monopoles with rational maps. The construction is based on the Nahm transform, which relates monopole chains to Higgs bundles on the cylinder. As an application, we classify charge k monopole chains which are invariant under actions of Z(2k). We present images of these symmetric monopole chains that were constructed using a numerical Nahm transform. Crown Copyright (C) 2022 Published by Elsevier B.V.
查看更多>>摘要：We identify Feigin-Odesskii brackets qn,1(C), associated with a normal elliptic curve of degree n, C C Pn-1, with the skew-symmetric n x n matrix of quadratic forms introduced by Fisher in [6] in connection with some minimal free resolutions related to the secant varieties of C. On the other hand, we show that for odd n, the generators of the ideal of the secant variety of C of codimension 3 give a Cremona transformation of Pn-1, generalizing the quadro-cubic Cremona transformation of P-4. We identify this transformation with the one considered in [14] and find explicit formulas for the inverse transformation. We also find polynomial formulas for Cremona transformations from [14] associated with higher rank bundles on C.(C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We study conformal Riemannian maps between the Riemannian manifolds. We derive a Bochner type identity and conditions for such maps to be harmonic. Later, we study conformal Riemannian maps whose total manifold admits a Ricci soliton and present a non-trivial example of such conformal Riemannian maps. We also obtain conditions for fiber and range space of such maps to be Ricci soliton and Einstein. We derive conditions for conformal Riemannian maps whose total manifold admits a Ricci soliton to be harmonic and biharmonic. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we study Lorentz-Sasakian space forms admitting conformal Ricci soliton and conformal gradient Ricci soliton. We also study the conditions for the soliton to be steady, shrinking and expanding. We also showed that depending on the nature of the structure function of Lorentz-Sasakian space form, the potential function of conformal gradient Ricci soliton is constant. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：For a simply connected closed Riemannian manifold with positive scalar curvature, we prove an upper diameter bound in terms of its scalar curvature integral, the Yamabe constant and the dimension of the manifold. When a manifold has a conformal immersion into a sphere, the dependency on the Yamabe constant is not necessary. The power of scalar curvature integral in these diameter estimates is sharp and it occurs at round spheres with canonical metric. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The aim of this paper is to show how we can induce contact structures, contact metric structures and Sasaki structures on a null hypersurface from a rigging vector field. We give several explicit examples of this construction and some obstructions to its existence. For example, contact metric structures can be introduced only on zero null mean curvature null hypersurfaces, whereas Sasaki structures can only be introduced in totally geodesic ones. In particular we show how we can construct a Kahler halo around an isolated horizon of a black hole. We also study the stability of the construction. We prove that close enough contact metric (resp. Sasaki) structures can be connected by a one parameter family of contact metric (resp. Sasaki) structures.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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