• Title, Summary, Keyword: concurrent vector field

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EUCLIDEAN SUBMANIFOLDS WITH CONFORMAL CANONICAL VECTOR FIELD

  • Chen, Bang-Yen;Deshmukh, Sharief
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1823-1834
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    • 2018
  • The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component $x^T$ of the position vector field is the most natural vector field tangent to the Euclidean submanifold M. We simply call the vector field $x^T$ the canonical vector field of the Euclidean submanifold M. In earlier articles [4,5,9,11,12], we investigated Euclidean submanifolds whose canonical vector fields are concurrent, concircular, torse-forming, conservative or incompressible. In this article we study Euclidean submanifolds with conformal canonical vector field. In particular, we characterize such submanifolds. Several applications are also given. In the last section we present three global results on complete Euclidean submanifolds with conformal canonical vector field.

The structure conformal vector fields on a sasakian manifold II

  • Hyun, Jong-Ik
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.661-679
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    • 1995
  • The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.

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SOME RESULTS ON CONCIRCULAR VECTOR FIELDS AND THEIR APPLICATIONS TO RICCI SOLITONS

  • CHEN, BANG-YEN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1535-1547
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    • 2015
  • A vector field on a Riemannian manifold (M, g) is called concircular if it satisfies ${\nabla}X^v={\mu}X$ for any vector X tangent to M, where ${\nabla}$ is the Levi-Civita connection and ${\mu}$ is a non-trivial function on M. A smooth vector field ${\xi}$ on a Riemannian manifold (M, g) is said to define a Ricci soliton if it satisfies the following Ricci soliton equation: $$\frac{1}{2}L_{\xi}g+Ric={\lambda}g$$, where $L_{\xi}g$ is the Lie-derivative of the metric tensor g with respect to ${\xi}$, Ric is the Ricci tensor of (M, g) and ${\lambda}$ is a constant. A Ricci soliton (M, g, ${\xi}$, ${\lambda}$) on a Riemannian manifold (M, g) is said to have concircular potential field if its potential field is a concircular vector field. In the first part of this paper we determine Riemannian manifolds which admit a concircular vector field. In the second part we classify Ricci solitons with concircular potential field. In the last part we prove some important properties of Ricci solitons on submanifolds of a Riemannian manifold equipped with a concircular vector field.

ON QUASI RICCI SYMMETRIC MANIFOLDS

  • Kim, Jaeman
    • Korean Journal of Mathematics
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    • v.27 no.1
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    • pp.9-15
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    • 2019
  • In this paper, we study a type of Riemannian manifold, namely quasi Ricci symmetric manifold. Among others, we show that the scalar curvature of a quasi Ricci symmetric manifold is constant. In addition if the manifold is Einstein, then its Ricci tensor is zero. Also we prove that if the associated vector field of a quasi Ricci symmetric manifold is either recurrent or concurrent, then its Ricci tensor is zero.

Super Quasi-Einstein Manifolds with Applications to General Relativity

  • Mallick, Sahanous
    • Kyungpook Mathematical Journal
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    • v.58 no.2
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    • pp.361-375
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    • 2018
  • The object of the present paper is to study super quasi-Einstein manifolds. Some geometric properties of super quasi-Einstein manifolds have been studied. We also discuss $S(QE)_4$ spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a super quasi-Einstein spacetime.

Efficiency Evaluation of Nozawa-Style Black Light Trap for Control of Anopheline Mosquitoes

  • Lee, Hee-Il;Seo, Bo-Youl;Shin, E-Hyun;Burkett, Douglas A.;Lee, Jong-Koo;Shin, Young-Hack
    • The Korean Journal of Parasitology
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    • v.47 no.2
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    • pp.159-165
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    • 2009
  • House-residual spraying and insecticide-treated bed nets have achieved some success in controlling anthropophilic and endophagic vectors. However, these methods have relatively low efficacy in Korea because Anopheles sinensis, the primary malaria vector, is highly zoophilic and exophilic. So, we focused our vector control efforts within livestock enclosures using ultraviolet black light traps as a mechanical control measure. We found that black light traps captured significantly more mosquitoes at 2 and 2.5 m above the ground (P<0.05). We also evaluated the effectiveness of trap spacing within the livestock enclosure. In general, traps spaced between 4 and 7m apart captured mosquitoes more efficiently than those spaced closer together (P>0.05). Based on these findings, we concluded that each black light trap in the livestock enclosures killed 7,586 female mosquitoes per trap per night during the peak mosquito season (July-August). In May-August 2003, additional concurrent field trials were conducted in Ganghwa county. We got 74.9% reduction (P<0.05) of An. sinensis in human dwellings and 61.5% reduction (P>0.05) in the livestock enclosures. The black light trap operation in the livestock enclosures proved to be an effective control method and should be incorporated into existing control strategies in developed countries.