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Benchmarking component choices for unpaired single cell RNA and epigenomic integration. [PDF]

Genome Biol
Naqing F, Yuan Q, Duren Z.
europepmc   +1 more source

Gluing constructions for Lorentzian length spaces. [PDF]

Manuscr Math
Beran T, Rott F.
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TOTALLY GEODESIC SUBMANIFOLDS OF GL-MANIFOLDS

International Journal of Geometric Methods in Modern Physics, 2012
In this paper, for a Finsler manifold (M, F) with a Finsler metric gij(x, y) we shall consider a generalized Lagrange metrics (FGL-metrics) as the form *gij(x, y) = gij(x, y) + σ(x, y)Bi(x, y)Bj(x, y) on TM. Then we shall consider a Riemannian manifold (TM, *G) in which *G is a generalized Sasakian metric of *g on [Formula: see text]. Then we restrict
Laleh, Abolghasem, Rezaii, Morteza M., Hushmandi, Ataabak Baagherzadeh   +2 more
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Congruences of totally geodesic surfaces

Classical and Quantum Gravity, 1989
A congruence of m-dimensional surfaces on a manifold M is a family of m- dimensional submanifolds which foliates M. Let (M,g) be a pseudo- Riemannian manifold. If every leaf is a totally geodesic submanifold, the congruence is said totally geodesic. The surface has rank k (\(\leq m)\) if at each point the induced ``metric'' has rank k.
Plebański, Jerzy F., Rózga, Krzysztof
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The Scalar Curvature on Totally Geodesic Fiberings

Annals of Global Analysis and Geometry, 2000
A compact Riemannian manifold \(N\) with scalar curvature \(\kappa _n\) is said to satisfy a comparison theorem for the scalar curvature iff for any other compact Riemannian manifold \(M\) (\(\dim M = \dim N\)) the inequality \(\kappa _M(x)\leq\kappa _N(f(x))\) holds at some \(x\in M\) whenever \(f:M\to N\) is a vector contracting spin map of non-zero ...
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TOTALLY GEODESIC SURFACES AND QUADRATIC FORMS

Journal of Knot Theory and Its Ramifications, 2013
Let M be a compact, connected, irreducible, orientable 3-manifold with torus boundary. A closed, orientable, immersed, incompressible surface F in M with no incompressible annulus joining F and ∂M compresses in at most finitely many Dehn fillings M(α).
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On totally geodesic affine immersions

Journal of Geometry, 1993
The author studies totally geodesic affine immersions into manifolds of recurrent curvature. In particular he gives sufficient conditions for the projective flatness of the submanifold. Examples are given for the classes of submanifolds studied.
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Laplacian on a totally geodesic foliation

Journal of Geometry, 1997
The work of \textit{L. Bérard-Bergery} and \textit{J.-P. Bourguignon} [Lect. Notes Math. 838, 30-35 (1981; Zbl 0437.53030)] on the Laplace-Beltrami operator acting on functions defined on the total space of a Riemannian submersion with totally geodesic fibers is extended to totally geodesic, bundle-like foliations \({\mathcal F}\) on a compact ...
Kang, Tae Ho, Pak, Hong Kyung, Pak, Jin Suk   +2 more
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Totally geodesic holomorphic subspaces

Nonlinear Analysis: Real World Applications, 2007
The author studies totally geodesic holomorphic subspaces in a complex Finsler space with respect to a complex Berwald connection. The equations of the holomorphic subspace have simple expressions. The totally geodesic subspaces are characterized by using the second fundamental form of the complex Berwald connection.
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Riemannian and Totally Geodesic Foliations

1988
The transversal geometry of a foliation is the geometry infinitesimally modeled by Q, while the tangential geometry is infinitesimally modeled by L. A key fact is the existence of the Bott connection in Q defined by $$ {\mathop{\nabla }\limits^{^\circ }_{{{X^S}}}} = \pi [X,{Y_S}]\,{\text{for}}\,X \in \Gamma L,\,s \in \Gamma Q $$ (5.1) where ...
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