scholarly journals Nonpositive curvature foliations on 3-manifolds with bounded total absolute curvature of leaves

2019 ◽  
Vol 11 (4) ◽  
pp. 1-17
Author(s):  
Dmytry Bolotov
Keyword(s):  
Negative Curvature ◽  
Positive Curvature ◽  
Nonpositive Curvature ◽  
Riemannian Metric ◽  
Geometric Properties ◽  
3 Dimensional ◽  
Total Absolute Curvature ◽  
New Class ◽  
Absolute Curvature

In this paper we introduce a new class of foliations on Rie-mannian 3-manifolds, called B-foliations, generalizing the class of foliations of non-negative curvature. The leaves of B-foliations have bounded total absolute curvature in the induced Riemannian metric. We describe several topological and geometric properties of B-foliations and the structure of closed oriented 3-dimensional manifolds admitting B-foliations with non-positive curvature of leaves.

scholarly journals Remarkable Classes of Almost 3-Contact Metric Manifolds

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 8
Author(s):  
Giulia Dileo
Keyword(s):  
Geometric Properties ◽  
New Class ◽  
Contact Metric Manifolds ◽  
Cosymplectic Manifolds ◽  
Sasaki Manifolds

We introduce a new class of almost 3-contact metric manifolds, called 3-(0,δ)-Sasaki manifolds. We show fundamental geometric properties of these manifolds, analyzing analogies and differences with the known classes of 3-(α,δ)-Sasaki (α≠0) and 3-δ-cosymplectic manifolds.

Projective flatness of a new class of ( α , β ) (\alpha,\beta) -metrics

2019 ◽  
Vol 26 (1) ◽  
pp. 133-139
Author(s):  
Laurian-Ioan Pişcoran ◽  
Vishnu Narayan Mishra
Keyword(s):  
Riemannian Metric ◽  
Real Scalar ◽  
New Class ◽  
Alpha Beta ◽  
Beta 2 ◽  
Projective Flatness ◽  
The Relationship

Abstract In this paper we investigate a new {(\alpha,\beta)} -metric {F=\beta+\frac{a\alpha^{2}+\beta^{2}}{\alpha}} , where {\alpha=\sqrt{{a_{ij}y^{i}y^{j}}}} is a Riemannian metric; {\beta=b_{i}y^{i}} is a 1-form and {a\in(\frac{1}{4},+\infty)} is a real scalar. Also, we investigate the relationship between the geodesic coefficients of the metric F and the corresponding geodesic coefficients of the metric α.

Negative Gaussian curvature induces significant suppression of thermal conduction in carbon crystals

Nanoscale ◽  
2017 ◽  
Vol 9 (37) ◽  
pp. 14208-14214 ◽  
Author(s):  
Zhongwei Zhang ◽  
Jie Chen ◽  
Baowen Li
Keyword(s):  
Gaussian Curvature ◽  
Thermal Conduction ◽  
Negative Curvature ◽  
Positive Curvature ◽  
Significant Suppression ◽  
Carbon Allotropes ◽  
Zero Curvature ◽  
Negative Gaussian Curvature

From the mathematic category of surface Gaussian curvature, carbon allotropes can be classified into three types: zero curvature, positive curvature, and negative curvature.

scholarly journals (n-2)-tightness and curvature of submanifolds with boundary

1978 ◽  
Vol 1 (4) ◽  
pp. 421-431 ◽  
Author(s):  
Wolfgang Kühnel
Keyword(s):  
Euclidean Space ◽  
Geometric Inequality ◽  
Total Absolute Curvature ◽  
Absolute Curvature

The purpose of this note is to establish a connection between the notion of(n−2)-tightness in the sense of N.H. Kuiper and T.F. Banchoff and the total absolute curvature of compact submanifolds-with-boundary of even dimension in Euclidean space. The argument used is a certain geometric inequality similar to that of S.S. Chern and R.K. Lashof where equality characterizes(n−2)-tightness.

Classification of 3-dimensional left-invariant almost paracontact metric structures

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Giovanni Calvaruso ◽  
Antonella Perrone
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Complete Classification ◽  
Natural Assumption ◽  
Geometric Properties ◽  
3 Dimensional ◽  
Metric Structures

AbstractWe study left-invariant almost paracontact metric structures on arbitrary three-dimensional Lorentzian Lie groups. We obtain a complete classification and description under a natural assumption, which includes relevant classes as normal and almost para-cosymplectic structures, and we investigate geometric properties of these structures.

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