Shiva did not kill Parvati. In Hindu mythology, Shiva is the husband of Parvati and they are considered a divine couple.
They have 2 sons, Ganesha and Murugan/Karttikey.
There are differing interpretations in Hindu mythology about whether Shiva cheated on Parvati during their relationship. Some stories suggest that Shiva had other relationships, while others emphasize his devotion to Parvati.
Parvati was the wife of Shiva, and the mother of Ganesh and Skanda. There are a multitude of names given for Parvati, such as Sahana, Shailaja, and Girirajaputri. Her counterpart in Vaishnavism is Lakshmi. See the link below for more information on Parvati.
Parvati gave birth to Ganesha when Lord Shiva was away. One day Parvati went for a bath and asked Ganesha to stand Guard. Suddenly Lord Shiva came and tried to enter the house. Ganesha could not recognize his father and obstructed his path. Lord Shiva got angry and beheaded Ganesha.
The family members of Lord Shiva include his wife Parvati, sons Ganpati (Ganesha) and Karthikeyan (Kartikeya).
Parvati is the wife of the Hindu god Shiva. Her name means "she of the mountains"
Parvati (wife of lord shiva)
The wives of Shiva in Hindu mythology are Parvati, Sati, and Shakti.
The consort of Shiva is Parvati aka Gouri.
ashok sundari is the daughter of shiva and parvati.
Derived from the name "Pragyaparomita," one of the names of Goddess Parvati, the name indicates the friend who will help you to go to heaven. Since Parvati is the wife of Shiva, and Shiva and his Yamdoots are related to death, Parvati is the one who shows the gates to Heaven.
Shiva, the Hindu god, is typically believed to have one wife, Parvati.