• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.505-517
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• 2002

We introduce certain conformally invariant h-Finsler connection in a Rizza manifold. Using this connection, we find some conformally invariant Finsler tensors. The conformal flatness and the Kaehlerian Finsler manifold with respect to the above connection are investigated.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.163-176
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• 2016

The object of the present paper is to introduce a new curvature tensor, named generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of generalized quasi-conformal curvature tensor are studied in the frame of (k, ${\mu}$)-contact metric manifolds.

• Communications of the Korean Mathematical Society
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• v.3 no.2
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• pp.231-248
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• 1988

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.287-304
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• 2016

In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of ${\mathbb{R}}^n$, $n{\geq}3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function H(x) is ${\beta}{\in}[1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.857-864
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• 2009

The special conformally flatness is a generalization of a sub-projective space. B. Y. Chen and K. Yano ([4]) showed that every canal hypersurface of a Euclidean space is a special conformally flat space. In this paper, we study the conditions for the base space B is special conformally flat in the conharmonically flat warped product space $B^n{\times}f\;R^1$.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.455-463
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• 1996

In [3] and [4], Kitahara, Pak and the author obtained the conformally invariant tensor $B_0$, which is an algebraic Hermitian analogue of the Weyl conformal curvature tensor W in the Riemannian geometry, by the decomposition of the curvature tensor H of the Hermitian connection and the notion of semi-curvature-like tensors of Tanno (see[7]). In [5], the author defined a conformally invariant tensor $B_0$ on a Hermitian manifold as a modification of $B_0$. Moreover he introduced the notion of local conformal Hermitian-flatness of Hermitian manifolds and proved that the vanishing of this tensor $B_0$ together with some condition for the scalar curvatures is a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.611-622
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• 2023

In this paper, we prove that every weakly Einstein slope metric, which is conformally flat on a manifold M of dimension n ≥ 3, is either a locally Minkowski metric or a Riemannian metric. We also prove the same result for conformally flat weakly Einstein Kropina metrics.

• The Journal of Korean Society for Radiation Therapy
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• v.17 no.2
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• pp.155-160
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• 2005

Purpose : Many authors have been introduced field in field technique and 3-D conformal radiotherapy that increased the tumor dose as well as decreased the dose of abutting critical organ. These technique have multiple beam direction and small beam segments even below 10 MU(monitor unit)for each field. we have confirmed the influence of low MU on dose output and beam stability. Materials and Methods : To study the dose output, the dose for each field was always 90MU, but it divided into different segment size: 1, 2, 3, 5, 10, 15 segments, 90, 45, 30, 18, 9, 6 MU the measurements were carried out for X-ray energy 4 MV, 6 MV, 10 MV of three LINAC(Varian 600C, 2100C, 2100C, 2100C/D), in addition each measurement was randomly repeated three times for each energy. To study the field symmetry and flatness, X-omat V films were irradiated. After being developed, films were scanned and analyzed using densitometer. Results : Influence of low MU on dose is slightly more increase output about $1.2{\sim}2.9%$ in cGy/mu than 90MU, but may not changed beam quality(flatness or symmetry), Output stability depends on dose rate(PRF)rather than beam energy, field size. Conclusion : Presented result are under the limits(out put<3%, flatness<${\pm}3%$, symmetry<2%). The 3 accelerators are safe to use and to perform conformal radiotherapy treatments in small segments, small MU around 10MU. but Even if the result presented here under the limits, continuous adjustments and periodic QA should be done for use of small MU