On the geometry of the manifold* g-SEX n and its conformal change

1991 ◽  
Vol 106 (11) ◽  
pp. 1271-1286
Author(s):  
Kyung Tae Chung ◽  
Dong Kum Jun
Keyword(s):  
Conformal Change

Conformai Curvature Tensors

2011 ◽  
Author(s):  
Charles Fefferman ◽  
C. Robin Graham
Keyword(s):  
Normal Form ◽  
Curvature Tensor ◽  
Riemannian Metric ◽  
Conformal Group ◽  
Conformal Change ◽  
Conformal Curvature ◽  
Covariant Derivatives ◽  
Curvature Tensors ◽  
Derivatives Of

This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to g. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group O(p + 1, q + 1) on tensors. It is assumed throughout this chapter that n ≥ 3.

scholarly journals Optical Detection of Vapor Mixtures Using Structurally Colored Butterfly and Moth Wings

Sensors ◽  
2019 ◽  
Vol 19 (14) ◽  
pp. 3058 ◽  
Author(s):  
Gábor Piszter ◽  
Krisztián Kertész ◽  
Zsolt Bálint ◽  
László Péter Biró
Keyword(s):  
Capillary Condensation ◽  
Principal Component ◽  
Sensor Material ◽  
Conformal Change ◽  
Vapor Sensing ◽  
Optical Responses ◽  
Surrounding Atmosphere ◽  
Vapor Mixtures ◽  
Chemically Selective ◽  
Wing Scales

Photonic nanoarchitectures in the wing scales of butterflies and moths are capable of fast and chemically selective vapor sensing due to changing color when volatile vapors are introduced to the surrounding atmosphere. This process is based on the capillary condensation of the vapors, which results in the conformal change of the chitin-air nanoarchitectures and leads to a vapor-specific optical response. Here, we investigated the optical responses of the wing scales of several butterfly and moth species when mixtures of different volatile vapors were applied to the surrounding atmosphere. We found that the optical responses for the different vapor mixtures fell between the optical responses of the two pure solvents in all the investigated specimens. The detailed evaluation, using principal component analysis, showed that the butterfly-wing-based sensor material is capable of differentiating between vapor mixtures as the structural color response was found to be characteristic for each of them.

scholarly journals Energy <i>β</i>-Conformal Change and Special Finsler Spaces

2013 ◽  
Vol 04 (07) ◽  
pp. 983-990
Author(s):  
Amr Soleiman ◽  
Amira A. Ishan
Keyword(s):  
Finsler Spaces ◽  
Conformal Change

scholarly journals The Chern–Ricci Flow on Oeljeklaus–Toma Manifolds

2017 ◽  
Vol 69 (1) ◽  
pp. 220-240 ◽  
Author(s):  
Tao Zheng
Keyword(s):  
Evolution Equation ◽  
Ricci Flow ◽  
Kodaira Dimension ◽  
Complex Manifolds ◽  
Hermitian Metrics ◽  
Conformal Change ◽  
Compact Complex Manifolds ◽  
Negative Kodaira Dimension

AbstractWe study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus–Toma (OT-) manifolds that are non-Kähler compact complex manifolds with negative Kodaira dimension. We prove that after an initial conformal change, the flow converges in the Gromov–Hausdorff sense to a torus with a flat Riemannianmetric determined by the OT-manifolds themselves.

scholarly journals GENERALIZED β-CONFORMAL CHANGE AND SPECIAL FINSLER SPACES

2012 ◽  
Vol 09 (03) ◽  
pp. 1250016 ◽  
Author(s):  
NABIL L. YOUSSEF ◽  
S. H. ABED ◽  
S. G. ELGENDI
Keyword(s):  
Finsler Metrics ◽  
Finsler Spaces ◽  
Conformal Change ◽  
Special Cases

This work is a continuation of the paper [Generalized beta-conformal change of Finsler metrics, Int. J. Geom. Meth. Mod. Phys. 7(4) (2010) 565–582]. In the present paper, we investigate the change of Finsler metrics [Formula: see text] which we refer to as a generalized β-conformal change. Under this change, we study some special Finsler spaces, namely, quasi-C-reducible, semi-C-reducible, C-reducible, C2-like, S3-like and S4-like Finsler spaces. We obtain some characterizations of the energy β-change, the Randers change and the Kropina change. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized β-conformal change, which we call the b-condition, and investigate the geometric consequences of such a condition. Finally, we give the conditions under which a generalized β-conformal change is projective and generalize some known results in the literature.

ENERGY β-CONFORMAL CHANGE IN FINSLER GEOMETRY

2012 ◽  
Vol 09 (04) ◽  
pp. 1250029 ◽  
Author(s):  
A. SOLEIMAN
Keyword(s):  
Vector Field ◽  
Finsler Geometry ◽  
Linear Connection ◽  
Finsler Manifold ◽  
Free Form ◽  
Cartan Connection ◽  
Chern Connection ◽  
Conformal Change ◽  
Berwald Connection ◽  
Curvature Tensors

The present paper deals with an intrinsic generalization of the conformal change and energy β-change on a Finsler manifold (M.L.), namely the energy β-conformal change ([Formula: see text] with [Formula: see text]; [Formula: see text] being a concurrent π-vector field and σ(x) is a function on M). The relation between the two Barthel connections Γ and [Formula: see text], corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy β-conformal change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is obtained. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.

Sign in / Sign up

Export Citation Format

Share Document