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The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [5], provides a way of representing immersed surfaces in $ℝ^{3}$ , and equipping the set of these immersions with a “distance function" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under reparametrizations (i.e., under self-diffeomorphisms of the domain surface) and under rigid motions of $ℝ^{3}$ . Thus, it induces a distance function on the shape space of immersions, i.e., the space...

Closed transverse $(p, p)$ -forms on compact complex manifolds

Lucia Alessandrini, Marco Andreatta (1987)

Compositio Mathematica

Cluster ensembles, quantization and the dilogarithm

Vladimir V. Fock, Alexander B. Goncharov (2009)

Annales scientifiques de l'École Normale Supérieure

A cluster ensemble is a pair $(𝒳, 𝒜)$ of positive spaces (i.e. varieties equipped with positive atlases), coming with an action of a symmetry group $Γ$ . The space $𝒜$ is closely related to the spectrum of a cluster algebra [12]. The two spaces are related by a morphism $p : 𝒜 \to 𝒳$ . The space $𝒜$ is equipped with a closed $2$ -form, possibly degenerate, and the space $𝒳$ has a Poisson structure. The map $p$ is compatible with these structures. The dilogarithm together with its motivic and quantum avatars plays a central role...

Coalgebraic Approach to the Loday Infinity Category, Stem Differential for $2 n$ -ary Graded and Homotopy Algebras

Mourad Ammar, Norbert Poncin (2010)

Annales de l’institut Fourier

We define a graded twisted-coassociative coproduct on the tensor algebra the desuspension space of a graded vector space $V$ . The coderivations (resp. quadratic “degree 1” codifferentials, arbitrary odd codifferentials) of this coalgebra are 1-to-1 with sequences of multilinear maps on $V$ (resp. graded Loday structures on $V$ , sequences that we call Loday infinity structures on $V$ ). We prove a minimal model theorem for Loday infinity algebras and observe that the ${Lod}_{\infty}$ category contains the $L_{\infty}$ category as...

Coarse topology, enlargeability, and essentialness

Bernhard Hanke, Dieter Kotschick, John Roe, Thomas Schick (2008)

Annales scientifiques de l'École Normale Supérieure

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the $K$ -theory of the corresponding reduced $C^{*}$ -algebras. Our proofs do not depend on the Baum–Connes conjecture and provide independent confirmation for specific predictions derived from this conjecture.

Cocalibrated $G_{2}$ -manifolds with Ricci flat characteristic connection

Thomas Friedrich (2013)

Communications in Mathematics

Any 7-dimensional cocalibrated $G_{2}$ -manifold admits a unique connection $\nabla$ with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the $\nabla$ -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of $\nabla$ -parallel vector fields.

Codazzi structures induced by minimal affine immersions

H. Furuhata (2002)

Banach Center Publications

We give a necessary and sufficient condition for a Codazzi structure to be realized as a minimal affine hypersurface or a minimal centroaffine immersion of codimension two.

Codazzi tensors and equations of Monge-Ampère type on compact manifolds of constant sectional curvature.

V.I. Oliker, U. Simon (1983)

Journal für die reine und angewandte Mathematik

Codimension one foliations on complex tori

Marco Brunella (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.

Codimension one foliations without compact leaves.

Paul S. Schweitzer (1995)

Commentarii mathematici Helvetici

Codimension one minimal foliations and the fundamental groups of leaves

Tomoo Yokoyama, Takashi Tsuboi (2008)

Annales de l’institut Fourier

Let $ℱ$ be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold $M$ . We show that if the fundamental group of each leaf of $ℱ$ is isomorphic to $Z$ , then $ℱ$ is without holonomy. We also show that if $π_{2} (M) ≅ 0$ and the fundamental group of each leaf of $ℱ$ is isomorphic to $Z^{k}$ ( $k \in Z_{\geq 0}$ ), then $ℱ$ is without holonomy.

Codimension one symplectic foliations.

Omegar Calvo, Vicente Muñoz, Francisco Presas (2005)

Revista Matemática Iberoamericana

We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.

Codimension reduction for real submanifolds of a complex hyperbolic space.

Shin-Ichi Kawamoto (1994)

Revista Matemática de la Universidad Complutense de Madrid

We study real submanifolds of a complex hyperbolic space and prove a codimension reduction theorem.

Coefficients généralisés de séries principales sphériques et distributions sphériques sur G.../G... .

P. Delorme (1991)

Inventiones mathematicae

Cofinal families in certain function spaces

William Wistar Comfort (1988)

Commentationes Mathematicae Universitatis Carolinae

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