A basic inequality for submanifolds in a cosymplectic space form

For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely its sectional curvature and scalar curvature on one side; and its main extrinsic invariant, namely squared mean curvature on the other side. Some applications including inequalities between the intrinsic invariant $\delta_{M}$ and the squared mean curvature are given. The equality cases are also discussedComment: Latex 9 page

Radio Imaging of the NGC 1333 IRAS 4B Region

The NGC 1333 IRAS 4B region was observed in the 6.9 mm and 1.3 cm continuum with an angular resolution of about 0.4 arcseconds. IRAS 4BI was detected in both bands, and BII was detected in the 6.9 mm continuum only. The 1.3 cm source of BI seems to be a disk-like flattened structure with a size of about 50 AU. IRAS 4BI does not show any sign of multiplicity. Examinations of archival infrared images show that the dominating emission feature in this region is a bright peak in the southern outflow driven by BI, corresponding to the molecular hydrogen emission source HL 9a. Both BI and BII are undetectable in the mid-IR bands. The upper limit on the far-IR flux of IRAS 4BII suggests that it may be a very low luminosity young stellar object.Comment: To appear in the JKA