Volume 57, Issue 3
Notes on Conformal Metrics of Negative Curvature on Manifolds with Boundary

Rirong Yuan

J. Math. Study, 57 (2024), pp. 373-378.

Published online: 2024-10

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  • 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.

  • AMS Subject Headings

53C18, 53C20, 53C21, 57M50

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COPYRIGHT: © Global Science Press

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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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