• Journal of the Korean Physical Society
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• v.80
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• pp.20-29
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• 2022

We discuss various aspects of anisotropic gravity in (d+D)-dimensional spacetime, where D dimensions are treated as extra dimensions. It is based on the foliation preserving diffeomorphism invariance and anisotropic conformal invariance. The anisotropy is embodied by introducing a factor z which discriminates the scaling degree of the extra D dimensions against the d-dimensional base spacetime and Weyl scalar field which mediates the anisotropic scaling symmetry. There is no intrinsic scale but a physical scale M_* emerges as a consequence of spontaneous conformal symmetry breaking. We discuss interesting lower dimensional gravity theories obtained from our model. In a (d, D) = (2, 2) case, we suggest a UV-complete unitary quantum gravity which might become Einstein gravity in IR. In a certain (2,1) case, we obtain CGHS model. Some vacuum solutions are also obtained and we discuss an issue of 'size separation' between the base spacetime and the extra dimensions. The size separation means large distinction between the scales (e.g. cosmological constant) appearing in the base spacetime and the extra dimensions respectively.

• Korean Journal of Remote Sensing
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• v.18 no.3
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• pp.171-179
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• 2002

Sampling rates become inconsistent when spatial data in the spherical coordinate are resampled with respect to latitudinal or longitudinal degree for mathematical processes such as Fourier Transform, and this results in distortions of the processed data in the wavenumber domain. These distortions are more evident in the polar regions. An example is presented to show such distortions during the recovery process of free-air gravity anomalies from ERS-1 satellite radar altimeter data from the Barents Sea in the Russian Arctic, and a method is presented to minimize the distortion using the Lambert Conformal Conic map projection. This approach was found to enhance the free-air gravity anomalies in both data and wavenumber domains.

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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• pp.31-37
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• 1987

I want to focus on developments in the areas of general relativity and gauge theory. The topics to be considered are the singularity theorms of Hawking and Penrose, the positivity of mass, instantons on the four-dimensional sphere, and the string picture of quantum gravity. I should mention that I will not have time do discuss either classical mechanics or symplectic structures. This is especially unfortunate, because one of the roots of differential geometry is planted firmly in mechanics, Cf. [GS]. The French geometer Elie Cartan first formulated his invariant approach to geometry in a series of papers on affine connections and general relativity, Cf. [C]. Cartan was trying to recast the Newtonian theory of gravity in the same framework as Einstein's theory. From the historical perspective it is significant that Cartan found relativity a convenient framework for his ideas. As about the same time Hermann Weyl in troduced the idea of gauge theory into geometry for purposes much different than those for which it would ultimately prove successful, Cf. [W]. Weyl wanted to unify gravity with electromagnetism and though that a conformal structure would fulfill thel task but Einstein rebutted this approach.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.304-307
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• 2008

Two-dimensional Stokes flow due to the line source and line sink of same strength in semi-infinite flow region with free surface is analysed using complex variable theory and conformal mapping. Surface tension effects are included while gravity is neglected. From the results of analysis, flow pattern and free surface shape are obtained and velocity distribution on the free surface is determined with 2 independent parameters Ca (capillary number) and h (non-dimensionalized distance between source and sink). When the location of the sink is above the source, velocity on the free surface converges and a cusp occurs on the free surface for the value of Ca above some critical capillary number.

• Proceedings of the KSEEG Conference
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• 2000.04b
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• pp.308-310
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• 2000

Sampling rates become inconsistent when spatial data in spherical coordinate are re-sampled with respect latitudinal or longitudinal degree for mathematical processes such as Fourier Transfrom, and this results in the distrtions of the processed data in the wavenmber domain. This distortions are more evident in the polar regions. An example is presented to show such distortions during the recovery process of free-air gravity anomalies from ERSI radar atimeter data in Russian Arctic Barents Sea, and a method is present to minimize the distortion using Lambect Conformal Conic map projection.