Journal•ISSN: 0232-704X
Annals of Global Analysis and Geometry
Springer Science+Business Media
About: Annals of Global Analysis and Geometry is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Differential geometry & Scalar curvature. It has an ISSN identifier of 0232-704X. Over the lifetime, 1450 publications have been published receiving 20771 citations.
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327 citations
TL;DR: The condition that x has nonzero constant mean curvature H = H 0 is known to be equivalent to the fact that xis a critical point of a variational problem.
Abstract: Let \(x:{\text M}^{n}\rightarrow\,{\text R}^{n+1}\) be an immersion of an orientable, n-dimensional manifold \({\text M}^{n}\) into the euclidean space \({\text R}^{n+1}\). The condition that x has nonzero constant mean curvature H = H 0 is known to be equivalent to the fact that xis a critical point of a variational problem.
240 citations
TL;DR: In this article it was shown that an almost paracontact structure admits a connection with totally skew-symmetric torsion if and only if the Nijenhuis tensor of the structure is skew symmetric and the defining vector field is Killing.
Abstract: The canonical paracontact connection is defined and it is shown that its torsion is the obstruction the paracontact manifold to be paraSasakian. A $${\mathcal{D}}$$
-homothetic transformation is determined as a special gauge transformation. The η-Einstein manifold are defined, it is proved that their scalar curvature is a constant, and it is shown that in the paraSasakian case these spaces can be obtained from Einstein paraSasakian manifolds with $${\mathcal{D}}$$
-homothetic transformations. It is shown that an almost paracontact structure admits a connection with totally skew-symmetric torsion if and only if the Nijenhuis tensor of the paracontact structure is skew-symmetric and the defining vector field is Killing.
229 citations
TL;DR: In this article, continuity for weighted modulation spaces is discussed, and it is shown that many such spaces can be obtained in a canonical way from the corresponding standard modulation spaces, and the trace operator a↦a(0, ·) acting on modulationspaces.
Abstract: We discuss continuity for weighted modulation spaces, andprove that many such spaces can be obtained in a canonicalway from the corresponding standard modulation spaces. We also discussthe trace operator a↦a(0, ·) acting on modulationspaces. The results are used to get inclusions betweenmodulation spaces and Besov spaces, and proving continuityfor pseudo-differential operators and Toeplitz operators.
178 citations
TL;DR: In this article, the authors studied the geodesic exponential maps corresponding to Sobolev type right-invariant (weak) Riemannian metrics μ(k) (k≥ 0) on the Virasoro group Vir and showed that each of them defines a smooth Frechet chart of the unital element e ∈Vir.
Abstract: We study the geodesic exponential maps corresponding to Sobolev type right-invariant (weak) Riemannian metrics μ(k) (k≥ 0) on the Virasoro group Vir and show that for k≥ 2, but not for k = 0,1, each of them defines a smooth Frechet chart of the unital element e ∈Vir. In particular, the geodesic exponential map corresponding to the Korteweg–de Vries (KdV) equation (k = 0) is not a local diffeomorphism near the origin.
169 citations