Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2003.06565

On Horizontal Immersions of Discs in Fat Distributions of Type $(4,6)$

Aritra Bhowmick
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this article we discuss horizontal immersions of discs in certain corank-$2$ fat distributions on $6$-dimensional manifolds. The underlying real distribution of a holomorphic contact distribution on a complex $3$ manifold belongs to this class. The main result presented here says that the associated nonlinear PDE is locally invertible. Using this we prove the existence of germs of embedded horizontal discs.

Explore related subjects

math.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Aritra Bhowmick. 2021-08-15. On Horizontal Immersions of Discs in Fat Distributions of Type $(4,6)$. https://doi.org/10.1142/s1793525321500539

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On vector-valued multisymplectic forms

We obtain a standard local presentation for a vector-valued multisymplectic form on a smooth manifold, generalizing the known proof for polysymplectic forms. We show that vector-valued multisymplectic forms on a finite-dimensional real vector space form a non-unital operad. We prove an entropy inequality for partial compositions.

math.DG↗
arXiv2026

Scalar curvature growth on nonnegatively curved three-manifolds

Let $(M^3,g)$ be a complete, connected, noncompact Riemannian three-manifold without boundary and with nonnegative sectional curvature. We prove that its scalar-curvature integral over geodesic balls, divided by the radius, has a limit. In the one-ended case, \[ \lim_{r\to\infty}\frac1r\int_{B_p(r)}\operatorname{Scal}\,d V =8π\bigl(χ(M)-V_M\bigr)\le8π(1-V_M), \] where $V_M$ is the asymptotic volume ratio. In the one-ended case, we show that $χ(M)\in\{0,1\}$. Thus positive asymptotic volume ratio gives the value $8π(1-V_M)$, while in the collapsed case the value is determined by the topology of the end. No pole or scalar-curvature bound is assumed. The proof combines separate smooth approximations of the Busemann and distance functions, integrable negative curvature errors, and a determinant estimate on the level surfaces. An averaged boundary estimate then gives convergence of the integrated extrinsic curvature. In the two-ended case, the splitting theorem gives the exact limit $8πχ(N)$ for the compact surface factor $N$. The one-ended upper bound is attained for every prescribed asymptotic volume ratio in $[0,1]$, and the two-ended bound is also sharp.

math.DG↗
arXiv2026

Some results on weighted p-harmonic $\ell$-forms on weighted manifolds

Basing on new curvature conditions for the Bochner technique of Petersen-Wrink in \cite{PW21}, in this paper, we give some vanishing properties for weighted $L^Q$ $p$-harmonic $\ell$-forms on weighted manifolds, where $p>1, Q>p-1.$ These results generalize some previous theorems for $L^Q$ harmonic $\ell$-forms of Dung-Dung-Hung on the paper \cite{DDH25}.

math.DG↗