• Title, Summary, Keyword: quaternion projective space

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RICCI CURVATURE OF SUBMANIFOLDS IN A QUATERNION PROJECTIVE SPACE

  • Liu, Ximin;Dai, Wanji
    • Communications of the Korean Mathematical Society
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    • v.17 no.4
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    • pp.625-633
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    • 2002
  • Recently, Chen establishes sharp relationship between the k-Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. In this paper, we establish sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in quaternion projective spaces.

ON CURVATURE PINCHING FOR TOTALLY REAL SUBMANIFOLDS OF $H^n$(c)

  • Matsuyama, Yoshio
    • Journal of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.321-336
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    • 1997
  • Let S be the Ricci curvature of an n-dimensional compact minimal totally real submanifold M of a quaternion projective space $HP^n (c)$ of quaternion sectional curvature c. We proved that if $S \leq \frac{16}{3(n -2)}c$, then either $S \equiv \frac{4}{n - 1}c$ (i.e. M is totally geodesic or $S \equiv \frac{16}{3(n - 2)}c$. All compact minimal totally real submanifolds of $HP^n (c)$ satisfy in $S \equiv \frac{16}{3(n - 2)}c$ are determined.

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Attitude and Position Estimation of a Helmet Using Stereo Vision (스테레오 영상을 이용한 헬멧의 자세 및 위치 추정)

  • Shin, Ok-Shik;Heo, Se-Jong;Park, Chan-Gook
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.7
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    • pp.693-701
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    • 2010
  • In this paper, it is proposed that an attitude and position estimation algorithm based on a stereo camera system for a helmet tracker. Stereo camera system consists of two CCD camera, a helmet, infrared LEDs and a frame grabber. Fifteen infrared LEDs are feature points which are used to determine the attitude and position of the helmet. These features are arranged in triangle pattern with different distance on the helmet. Vision-based the attitude and position algorithm consists of feature segmentation, projective reconstruction, model indexing and attitude estimation. In this paper, the attitude estimation algorithm using UQ (Unit Quaternion) is proposed. The UQ guarantee that the rotation matrix is a unitary matrix. The performance of presented algorithm is verified by simulation and experiment.