Applying the method of Moving Frames,we prove a famous Theorem due to N.Boken,K.Nomizu and U.Simon in :If M n(n≥2) is a nondegenerate affine hypersurface in A n+1 ,then both C and 2C are totally ...Applying the method of Moving Frames,we prove a famous Theorem due to N.Boken,K.Nomizu and U.Simon in :If M n(n≥2) is a nondegenerate affine hypersurface in A n+1 ,then both C and 2C are totally symmertric if and only if C=0 (M is a quadric) or S=0 (M is an improper affine hypersphere). Moreover,we improve the conditions of Theorem 2 and its Corollary in .also prove, if ^ C=0 and the affine metric G is of constant curvature α, then M is an affine hypersphere and a=0 or C=0.展开更多
The relationship between ENSO and Indian Ocean Dipole was discussed by using the data set of sea temperature from Scripps Institute of Oceanography, the air temperature at 1000hPa from the NCEP reanalysis data and the...The relationship between ENSO and Indian Ocean Dipole was discussed by using the data set of sea temperature from Scripps Institute of Oceanography, the air temperature at 1000hPa from the NCEP reanalysis data and the Nino3 index from the Climate Prediction Center （CPC） of U.S.A. during the period from 1955 to 2001. The results show that there exists a Dipole on the maximum temperature anomalous level （MTAL） in the Indian Ocean, which close relates to ENSO in the Pacific Ocean. During El Nino periods there are good relationships between ENSO and Indian Ocean Dipole which maximum correlation occurring when ENSO leads by one month, but in La Nina periods the relationship is not so good. The distribution of Dipole in Indian Ocean is from northeast to southwest, which one （west） pole in 65°E - 75°E, 6°S - 10°S and the other in 85°E - 95°E, 2°N - 6°N, which is different from that defined by Saij. The correlation coefficients of Nino3 index with temperature anomalies in the west/east poles on the MTAL are over 0.4 - 0.15, respectively. It is a main sea temperature system in the tropical Indian Ocean. However, in the surface layer from sea surface to the depth of 20 m - 30 m there is no such a dipole with opposite sea temperature anomalies in the NE and SW of tropical Indian Ocean. The SSTA in the NE might be influenced by the sensible exchange process because the evolution of sea and 1 000 hPa air temperature anomaly time series of the NE of tropical Indian Ocean is quite similar except those during 1962 - 1963 and 1986. The periods of Indian Ocean Dipole are shorter than that of ENSO, and about 1 to 6-year.展开更多
Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M...Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M , a sufficient condition is given for M as a flat torus in R 4 .展开更多
文摘Applying the method of Moving Frames,we prove a famous Theorem due to N.Boken,K.Nomizu and U.Simon in :If M n(n≥2) is a nondegenerate affine hypersurface in A n+1 ,then both C and 2C are totally symmertric if and only if C=0 (M is a quadric) or S=0 (M is an improper affine hypersphere). Moreover,we improve the conditions of Theorem 2 and its Corollary in .also prove, if ^ C=0 and the affine metric G is of constant curvature α, then M is an affine hypersphere and a=0 or C=0.
基金supported by the National Natural Science Foundation of China, (No. 40976015)National Basic Research Program of China under Grant No. (2010CB950302)
文摘The relationship between ENSO and Indian Ocean Dipole was discussed by using the data set of sea temperature from Scripps Institute of Oceanography, the air temperature at 1000hPa from the NCEP reanalysis data and the Nino3 index from the Climate Prediction Center （CPC） of U.S.A. during the period from 1955 to 2001. The results show that there exists a Dipole on the maximum temperature anomalous level （MTAL） in the Indian Ocean, which close relates to ENSO in the Pacific Ocean. During El Nino periods there are good relationships between ENSO and Indian Ocean Dipole which maximum correlation occurring when ENSO leads by one month, but in La Nina periods the relationship is not so good. The distribution of Dipole in Indian Ocean is from northeast to southwest, which one （west） pole in 65°E - 75°E, 6°S - 10°S and the other in 85°E - 95°E, 2°N - 6°N, which is different from that defined by Saij. The correlation coefficients of Nino3 index with temperature anomalies in the west/east poles on the MTAL are over 0.4 - 0.15, respectively. It is a main sea temperature system in the tropical Indian Ocean. However, in the surface layer from sea surface to the depth of 20 m - 30 m there is no such a dipole with opposite sea temperature anomalies in the NE and SW of tropical Indian Ocean. The SSTA in the NE might be influenced by the sensible exchange process because the evolution of sea and 1 000 hPa air temperature anomaly time series of the NE of tropical Indian Ocean is quite similar except those during 1962 - 1963 and 1986. The periods of Indian Ocean Dipole are shorter than that of ENSO, and about 1 to 6-year.
文摘Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M , a sufficient condition is given for M as a flat torus in R 4 .
