Liquid crystals formed by acute-angle bent core (ABC) molecules with a 1,7 naphthalene central core show an intriguing phase behavior with the nematic phase accompanied by poorly understood additional phases. In this work, we characterize the physical properties of an ABC material, such as birefringence, dielectric permittivities, elastic constants, and surface alignment and present x-ray diffraction and transmission electron microscopy studies of their ordering. The ABC molecular shape resembling the letter λ yields a very small splay elastic constant in the uniaxial nematic phase and results in the formation of a tetragonal positionally ordered columnar phase consisting of alternating polar and apolar molecular columns with a uniform uniaxial director that can be bent but not splayed.