I found this spider jumping around in my garden , to describe it is blue and black . I noticed that it has strong front legs and a pointed posterior , it has blue designs on a black body . I live in South India ,ie , a tropical region . It is approximately 1cm in length .
This looks to me like Thiania bhamoensis (Metallic Blue Jumper), whose species distribution includes India. It has a notably pointy abdomen, as you noted, and the listed size range appears to be consistent as well.
I do not believe this is Phidippus audax due to the colour inconsistency (only the chelicerae are blue) as well as the fact that the known species distribution lies entirely within North and South America.
This is Phidippus audax commonly known as Jumping spider or Daring Jumping spider.