Notes on Conformal Metrics of Negative Curvature on Manifolds with Boundary
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@Article{JMS-57-373,
author = {Yuan , Rirong},
title = {Notes on Conformal Metrics of Negative Curvature on Manifolds with Boundary},
journal = {Journal of Mathematical Study},
year = {2024},
volume = {57},
number = {3},
pages = {373--378},
abstract = {
We use certain Morse functions to construct conformal metrics such that the eigenvalue vector of modified Schouten tensor belongs to a given cone. As a result, we prove that any Riemannian metric on compact 3-manifolds with boundary is conformal to a compact metric of negative sectional curvature.
}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v57n3.24.08}, url = {http://global-sci.org/intro/article_detail/jms/23497.html} }
TY - JOUR
T1 - Notes on Conformal Metrics of Negative Curvature on Manifolds with Boundary
AU - Yuan , Rirong
JO - Journal of Mathematical Study
VL - 3
SP - 373
EP - 378
PY - 2024
DA - 2024/10
SN - 57
DO - http://doi.org/10.4208/jms.v57n3.24.08
UR - https://global-sci.org/intro/article_detail/jms/23497.html
KW - Schouten tensor, Modified Schouten tensor, conformal deformation, Morse theory.
AB -
We use certain Morse functions to construct conformal metrics such that the eigenvalue vector of modified Schouten tensor belongs to a given cone. As a result, we prove that any Riemannian metric on compact 3-manifolds with boundary is conformal to a compact metric of negative sectional curvature.
Yuan , Rirong. (2024). Notes on Conformal Metrics of Negative Curvature on Manifolds with Boundary.
Journal of Mathematical Study. 57 (3).
373-378.
doi:10.4208/jms.v57n3.24.08
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