Conformal Geometry of the Supercotangent and Spinor Bundles

In this paper, a novel wideband conformal fractal antenna is proposed for GPS application. The concepts of fractal and partial ground are used in conformal antenna design for miniaturization and bandwidth enhancement. It comprises of Minkowski fractal patch on a substrate of Rogers RT/duroid 5880 with permittivity 2.2 and thickness of 0.787mm with microstrip inset feed. The proposed conformal antenna has a patch dimension about 0.39λmm×0.39λmm, and partial ground plane size is 29mm×90mm.The proposed antenna is simulated, fabricated and measured for both planar and conformal geometry, with good agreement between measurements and simulations. The size of the fractal patch is reduced approximately by 32% as compared with conventional patch. It is observed that the conformal antenna exhibits a fractional bandwidth(for the definition of -10dB) of 43.72% operating from 1.09 to 1.7GHz, which is useful for L1(1.56-1.58GHz), L2(1.21-1.23GHz), L3(1.37-1.39GHz), L4(1.36-1.38GHz), and L5(1.16-1.18 GHz) in GPS and Galileo frequencies: E=1589.742MHz(4MHzbandwidth), E2=1561. 098MHz(4MHzbandwidth), E5a=1176.45MHz(=L5),E5b= 1207.14MHz, and E6=1278.75MHz(40MHz bandwidth). The radiation pattern exhibits an omnidirectional pattern, and gain of proposed antenna is 2.3dBi to 3.5dBi within operating frequency range.

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Conformal Geometry of Horn Angles of Second Order

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.24.9.393 ◽

1938 ◽

Vol 24 (9) ◽

pp. 393-400 ◽

Cited By ~ 1

Author(s):

E. Kasner ◽

J. de Cicco

Keyword(s):

Conformal Geometry ◽

Second Order

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An Interactive Indoor 3D Reconstruction Method Based on Conformal Geometry Algebra

Advances in Applied Clifford Algebras ◽

10.1007/s00006-018-0880-9 ◽

2018 ◽

Vol 28 (4) ◽

Author(s):

Niantao Liu ◽

Bingxian Lin ◽

Linwang Yuan ◽

Guonian Lv ◽

Zhaoyuan Yu ◽

...

Keyword(s):

3D Reconstruction ◽

Conformal Geometry ◽

Reconstruction Method

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Jordan algebras and conformal geometry

Positivity in Lie Theory ◽

10.1515/9783110811186.1 ◽

1998 ◽

pp. 1-20 ◽

Cited By ~ 1

Author(s):

Wolfgang Bertram

Keyword(s):

Conformal Geometry ◽

Jordan Algebras

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Behavior of a vacuum and naked singularity under a smooth gauge function in Lyra geometry

Canadian Journal of Physics ◽

10.1139/cjp-2017-0681 ◽

2018 ◽

Vol 96 (9) ◽

pp. 969-977

Author(s):

Haizhao Zhi

Keyword(s):

Physical Meaning ◽

Conformal Geometry ◽

Naked Singularity ◽

Lyra Geometry ◽

Space Time ◽

Gauge Function ◽

Weyl Geometry ◽

Irregular Singular Point ◽

New Space ◽

Symmetric Gauge

Lyra geometry is a conformal geometry that originated from Weyl geometry. In this article, we derive the exterior field equation under a spherically symmetric gauge function x0(r) and metric in Lyra geometry. When we impose a specific form of the gauge function x0(r), the radial differential equation of the metric component g00 will possess an irregular singular point (ISP) at r = 0. Moreover, we can apply the method of dominant balance to get the asymptotic behavior of the new space–time solution. The significance of this work is that we can use a series of smooth gauge functions x0(r) to modulate the degree of divergence of the singularity at r = 0, which will become a naked singularity under certain conditions. Furthermore, we investigate the physical meaning of this novel behavior of space–time in Lyra geometry and find out that no spaceship with finite integrated acceleration can arrive at this singularity at r = 0. The physical meaning of the gauge function and integrability is also discussed.

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